If there was a least helpful comment awards, this would be nominated. Although possibly not, it would be a very big fight for those nominations.
Anyway OP, there is no right way to play RE3. Running away from Nemesis and fighting him are equally valid (and imo entertaining) options. The right choice then is what is more natural to you, if you think running away is the best option, go for it. Nemesis is tough, and downing him is no easy task. And as you implied, it takes a lot of ammo and likely healing itens. So trying to put me in your position, I'd play hard and avoid Nemesid when I can. Your first fight with him only occurs later in the game, by that time you would have both the magnum and the granade laucher, either use gunpowder to make bullets for the magnum CCC (C being A + B) or freeze rounds (CC). The later is a cooler choice if you ask me. Although the former is possibly a more powerful combo.
If you do want to face Nemesis everytime, then play on easy. You get a lot of weapons that make facing him a much simpler task. Use the magnum and you should have a much easier time. He won't drop stuff though.
As for the dodge, just check this video:
But keep in mind. Although RE3's dodge is cool as hell, it's a... hard temperament. Against zombies it's very, very hard to pull of so just ignore it. The easiest enemy do dodge is actually Nemesis. You can practice dodges against him. But even against the monster it can be quite unreliable. So dodge should always be a last resort.