If cost is an issue, you're not going to find any revolver - other than a .22 - that is as cheap to feed as a 9mm auto. On a limited budget, you're also going to be stuck looking for used revolvers as well (at least if you want a Colt or S&W), which might mean that you'll get one that is actually going to be less reliable compared to a value priced semi auto pistol. You have to know what to look for when shopping for a used revolver, and if this is your first one, there might be a learning curve.

People complain about the cost of .357 Sig ammo at times, yet it is actually generally cheaper than .357 mag.

If you can find someone to take with you, go poke around and try to find a fixed sight K frame in .38 special. Load it with 158gr +P LSWCHP ammo - which you'll probably have to order. You'll also want to (heresy I know) put a Hogue monogrip or some such on it.

An L frame 686 or a Colt Python would be a better, probably top of the heap offering and you'd have a nice .357, but neither is cheap (even used/abused). Around here a decent shooting used 686 is 500 dollars or more.

Otherwise... Glock, Sigma or even (gasp) Hi Point 9mm pistols are going to be a better bet.