The newest game i would play would be like dead space, just looking for ideas. hd medium/max settings perferred

It'd help if people knew your price range.

I can't help on the tech side, all I can say is in 2015 I bought an old Dell WinVista laptop off Amazon (2 gig ram, 80 gig hd, but no battery and just integrated graphics) for 60 dollars and it runs DOSBox/ScummVM games pretty well (though I didn't play graphically invensive titles - Bio Menace, Duke Nukem 1, co.) and Flatout 1 ran okay. I'm sure Dead Space wouldn't work well though if at all.

This may help also - http://gamesystemrequirements.com/game/dead-space or you may want to check out the gamecard here: https://www.gog.com/game/dead_space

Price range would be like anything under $350 or something, idk

You may need to buy a used one then, like off eBay. Do you specifically want to be able to play Dead Space 1 on the go? Otherwise it looks like you could buy a PS3 for $100-150 (or even less) and the game for like $10.

Found quickly 2 close to budget: Intel $350 (i3-7100U, 4GB RAM, 1TB HDD, HD 620 GPU) and AMD $380 (A12-9720P, 8GB RAM, 1TB HDD, R7 GPU). Buying a desktop for that money would be a way better option for gaming.

So older than 2008, Crysis excluded? ;-)

Old(er) second hand laptop: you'd need one with a graphics card (Nvidia/ATI).
New(ish) laptop: integrated graphics should be able to run Dead Space at decent settings. I'd replace those 5,400rpm HDDs with an SSD. Although the main reason the OP mentions is to play old games - those slow HDDs will make them feel really sluggish.
The AMD one has a really crappy screen.

I'd go for something like this:
https://www.ebay.com/itm/Lenovo-ThinkPad-W540-15-6-FHD-2-90GHz-CORE-i7-4600M-16GB-240GB-SSD-W8PRO-WEBCAM/253490317270
Ok, it's 50$ over budget, but I just did a real quick search.
In this case, the Quadro GPU is something like a GT 750M. And Lenovo Thinkpad Workstations are really durable - IMO MUCH more preferable than some new cheap consumer laptop.

Considering he wants a laptop under $350, investing in a SSD just increases the price, or then he would have to get some stupid 125GB SSD that will be full in no time.

Also, to this day I still don't understand how some of you people praise SSD, as if it makes everything feel sooooo different.

I have now two gaming (capable) laptops. One has old 5400rpm HDDs, the other has a 256GB SSD. The games play the same on both, the only difference is the loading times. I simply couldn't care less if it takes 2 seconds or 10 seconds to load up a game. That is the only difference you will see while playing game, for having a SSD, yet some make it sound as if "upgrading" to a SSD is the biggest upgrade you could ever do for your gaming PC. I wrote "upgrading" because to me it feels more like a downgrade, as big SSDs just cost too much so one has to go with some measly 256GB SSD, unless they are ready to pay an arm and a leg for it.

SSDs just aren't worth the extra price for gaming, period. The more extra room you get for the same money by buying a HDD instead makes much more sense.

True. but then older games are smaller so they load very fast even on a HDD.

That's the dilemma I personally see with SSDs: their extra speed would be more useful with bigger amounts of data (like 50-100GB AAA games that load lots of data)... but they are so small that you can't keep that much data on them. Hence we see people buying an extra HDD on the side of their primary 128GB or 256GB SSD, and installing all their games on the bigger HDD. Then they don't really see the speed benefit even in game loading times.

In Windows 10 the Windows loads very fast also with HDDs because of the hibernate mode it uses by default (that's the trick MS has used in Windows 8 and later to make it appear it loads very fast compared to Windows 7: normally it is not closed down completely, but put into hibernate mode). I don't start Windows that often anyway, usually once a day.

Maybe some others are more susceptible to Windows loading times, I don't know. I care more for hard drive speeds if I am handling (e.g. compressing or uncompressing) hundreds of gigabytes of archived data, but unfortunately SSDs are not suitable for that either due to their size constraints ($ per gigabyte).

In need of same thing too

You didn't comment on the OS "sluggishness" when using a 5,400 rpm laptop drive. It's a lot worse than a (3,5") 7,200 rpm desktop HDD.
But like I said before, if you only care about the performance of the games themselves, then it's probably no big deal.

Not sure what that even is. How fast Notepad or command prompt starts when I click on their icons? To me Windows 7 doesn't feel sluggish on this HDD laptop where I am writing this, even compared to my SSD laptop (which is running Windows 10 though). Maybe I am less susceptible to it then.

I need fast hard drive when handling lots of data, like working with archives or playing 100 gigabyte AAA games.

I have friends and relative cast off computers.
The best one is an old Winbook XP laptop. It seems to play
the old games the best. You can still boot to DOS,
it has a CD drive, floppy drive, and 32 bit system.

Ask around, your friends or relative may have an old,
but still working computer in their closet, just waiting to
be used again. The price is usually low to free.

Have you considered OS other than Windows?

That's my case, I've got Lenovo and paid something around $300 back then. Buying without Windows saved me about 25-30% of overall price. And it saved me also a lot of nerves, dangers and time, because I've got still nice, quick Linux Mint Mate onboard and I'm happy playing most of games I want. Older games are usually easily available for Linux gamers. Wow, I had no idea that such specs are today available for that price! Looks quite optimistic for me ;) Fully agree.