I seem to be having issues progressing or making any kind of progress.

I seem to be constantly staying relatively in the same position and state.

If I do missions of appropriate level, I get average money and average expenses. If I choose harder missions I tend to nullify any financial bonus by my expenses. And if I choose easier missions, I tend to actually go backwards.

Basic tactics: Dont get internal damage! Therefor the first thing to do is, strip one weapon you dont need of mechs you get and max the armour. This costs no time and makes the mech really tougher. Do all low skull missions on one planet and balance loot versus money to your like (in late game i always go max loot, in earlier games it depends on payout). The more money a mission gives, the harder it will most likely be (not only th eskulls say something about difficulty).
When moving to your next planet remove useless weapons with better ones or repair internals. For me best for start are something like AC5, M-Lasers, SRMs and for better tactitcs get Jumpjets.
I like Bulwark most, combined with Jumpjets you most likely find wooden terrain to hide for 40% damage reduction while fighting or 60% while bracing (remember, dont get internal damage).
Conecentrate fire on mechs that can hurt you much, often thos are the ones that have weak armour. Use Called shot to middle torso whenever possible.
Have 6 warriors to 8 warriors at start game, better 6 first to save cash, some mechs you use, like 6-8 the rest in storage.
Send mechs to storage and sell them then. If playing the campaign, make sure to be prepared well for special missions, they give alot of cash. Once you have heavies, life gets easier.
My usual setup for mechs in midgame, Jumpjets, some mechs with AC20 that shoot first, some with lots of M-Lasers and/or SRM to do the final blows.
You can go LRM heavy as many people do, but you have to keep distance to enemy and missions take significantly longer, but chance to get 3 mech parts is higher.
Headshot or Legshot mechs or give them pilot damage to get more than one part out of a mech ;)

I have read this entire post... and i agree with it. I agree with it so much that, i can tell you right now that i do everything you already suggest. And have been doing it since the beginning of the game.

The list of suggestions was very good and if you're following them and still struggling, then something else must be the issue...

One good strategy I've employed in the early game is always skirting the edge of the map. You'll be facing two lances in most engagements. If you can get those two lances to face you one at a time, life is much easier. Skirting the map is much simpler with jumping mechs though, so I modify, sell, or store all non-jump enabled mechs.

And to re-emphasize one point Hohiro made: Add more armor! Internal damage cuts into your ability to make c-bills. But don't be afraid to use a "barely damaged" mech either. I often run Panthers as my early game light mech of choice with a Large Laser, SRM6, and 1-2 Medium Lasers so I can slap 600+ armor on 'em along with the jump jets. If it gets hot, go punch someone.

I honestly keep looking to see whether i have the game on a higher difficult than the lowest. Because for me, it is impossible to complete a contract without at least one of my mechs scoring internal damage, no matter how hard i try or what i do to try to avoid it.

And yes, internal damage removes any profit from that contract. It is so bad that the moment they get a lucky hit that incurs internal damage on any of my mechs, i just restart the mission. Simply because internal damage is so crushing to my funds.

A bit more careful, try to lure one or few in a certain place ... if no one can shoot on you, try sensor lock to make chances to hit better. One good armed always in front to tank damage. It works with practise.

I played Mech Commander 1 and 2. A couple times over. And a heck of a lot of strategy games including the recent Fire Emblem game too. This is how i usually play anyway. Heavily armoured unit up front to lure them in, then use my other units to pounce on them.

But it does not seem to work too well in this game.

Well if you fllowing these tactics it shouldnt be too hard .... hmmm .... you moving with your small units to get lots of evasion? Your mechwarriors are well trained? You hace few enough mechs and warriors ready? Locusts and other crap mechs are in storage and not ready? Probably avoid Martian and Lunar enviroments for lack of hiding places.
One thing I havent tried yet, try to get a mortar on one mech, artillery should help with less acuracy.

If you want, you can upload a savegame somewhere and I could look over it and check what I would change.

In scenarios, take time to see the land, where to go, by what way, then take the safer and stealth trail.
Be king of the wooden hill first.

For me, most difficult mission is intercept convoys. Any advice for those?

This mission is one wher e"reserve" is really good ... and later ECM ;)

Try to get in between place where they leave and them ... mechs often are faster than the vehicles, so you often can destroy one mechs till the vehicles reach you. When able to shoot at vehicles, destroy them ASAP, especially SRM, LRM, Demolisher, PPC carriers .... only problem: There are so many enemies, so when you reserve, there are often some having turns after you.
When one of your guys is being Sensorlocked, he is their prefered target, jump far inside some wood and brace. The others demolishing enemies (if only 1 or 2 are after you or others too far away).

At one mission, you can divide mechs and vehicles when there is a big mountain in between, mechs come towards you, you hit 1 or 2 and jump on the muntain. They cant follow and you take on the vehicles from above on the other side, then come back.

Edit: AC20 as aimed shot against a Demolishers side armour can kill it quite easily, SRM and LRM are very easy one shot kills, PPc quite easy if lucky.

100% agree with you re: king of the wooded hill over on the side of the map. :)

Re: Convoys - I'm a big fan of stomping on vehicles whenever possible. Lowers my heat to allow more alpha-strikes against the mech guards and it does double damage (weird mech vs vehicle bonus) which means that from the side or back, pretty much every vehicle will be killed with a single melee attack.

But yeah, sometimes you can't separate the guards from the convoy and one of those SRM/LRM carriers, AC20 beasts, or Shreck PPC carriers gets a shot or two on you. Those occasional missions are rough and when that map loads up, I know I'm in trouble. I wish the convoys I escorted had weapons (and armor) like that.

My single biggest issue is just how utterly shattering/crippling getting a single mech shot to shit with internal damage. It seriously kills the fun in the game when you go broke because your mechs took internal damage.

I have gone so far as to restart missions or just flat out quit the game right there and then when a mech takes internal damage BECAUSE it is so damn crippling to my wallet.

A bit of internal damage is ok, if you repair in between systems (but at beginning I prefer to upgrade). But getting one mech banged up pretty much doesnt happen that easy, if you progress carefully, have biggest mech as tank, have Bulwark, have max armour, get enough evasion, hide in forests, use Called Shot whenever useful, turn damaged sides away, kill mechs with high damage output and low armour quickly.

Sometimes it helps, if you disable the mechs main weapons (called shots at arm of a panther for example). For me there is no 100% always working way, I act depending on situation and what I have on stock.

Btw, Locust, Spider and such should never be in front, if you have to bring them on field. And if you have at some ocassions the need to do so really they need to move max.
Other strat for them is to wait till enemy has made moves, jump behind them, give a shot in the back, next turn jump away max distance in something to hide before the enemy moves or, if no other enemy is around, move and hit from behind again. The smalls just NEVER should stand still if they are target to an enemy, they will get hit tooooo easily.

You could take a look at some Lets Play videos to see where you have problems, I played campaign mode like 4 times whenever an expansion came out and several career mode and in all didnt have too much problems ... whenever you encounter some really bad mechs you can try to load the mission and geet other mechs, some randoms are just very unlucky for the player, but this doesnt happen regularly. A one star mission with few cash as reward should never get you internal damage.

are you staying in the same area? if you don't move around a little then the missions tend to dry up because that planet becomes stable