Shitty situations is the reason I'm surprised I finished RE0-3. RE3 wasn't a problem because I cheated with the Gameshark on DC but RE2 I played no cheats on PSX and RE0&1 I played on GC no cheats.
I'm the kinda person that'll give up on a game (or cheat) if I think it'll take too much time or effort getting through a certain area. I think it took me a while to beat RE1 or 0 because I got into some shitty situations with ammo and health but I managed to force myself through them because they usually rewarded you with more items after the battle or whatever.
To save ammo use the grenades. You rarely need to use them but I usually use them when I'm in a big battle. You'll know when you have to use one, usually that's all it takes to thin out a crowd.