I don't know if I missed something. I started playing sentinels. After finishing the third mission where you have to rescue the operative you get to hire for the first time the mercenaries. But i have not enough money to hire even the cheapest one.
Did I miss something? Don't you get some startup money?
So now I have to solo the random encouters to get money? This is frustratingly hard. I tried and often I have to pay more or roughly the same money for the healing in the base then I get from selling the weapons of the enemies.

No way to get sam stay in your team?

Sam - no way. You'll meet him again once, but that's all.

Well, it's kinda difficult with money, yes. Collect all loot and sell it. Search gold, pictures, banknots, pocket clocks and try not to miss random encounters.
Not a fair variant - use Artmoney to increase money or cheats to spawn a necessary weapon.

Yes, healing in the hospital room is extremely expensive. I finally decided to go on without using it. In fact, I haven't used it once, and I've fought dozens of encounters and a couple missions so far.

I hired the cheapest medic and, after some random encounters to level him up, he's starting to be quite competent. He can patch up almost anything while on the battlefield, and he provides thorough healing once we're back at the base. I also needed a medic anyway because I foolishly started a custom game with the "only heal based on medic healing skill" option (and, let me tell you, that makes things... spicy).

So, as long as you have a medic I think you shouldn't waste money on the hospital. AFAIK having all your guys with yellow health bars instead of green (as I do now) doesn't matter as long as the bars are filled. But, I'm not 100% sure about that. So far it's working nicely for me, though.