In need of a car-guy (or girl) opinion…

I have a 1996 Dodge Neon, and I think the fuel pump is dying, but I’m not a car guy. It chokes and sputters going up decent hills, and over 45 or 50 on flat roads on an average day (say, 70 degrees). I can go faster on cooler days, and maybe only 40-45 on hotter days. Like I said, I’m not a car guy, but I think it’s the fuel pump. Now, what do those things cost to replace, I’ve heard around $200, and might there be something less expensive to test first (like you change the thermostat first then your car is overheating on a full reservoir)?