I use a 1995 GT Outpost Trail. The Acera shifters are crap, they get gummed up easily, I expect you're experiencing this issue. Luckily you can find a pair of replacement shimano shifters for about $40; I forget the model number, they don't even belong to one of the groupsets, so they don't even have a name, but they're good. They look similar to the Alivio 8 speed shifters.
I wouldn't recommend shifting just using the front derailleur. I always had major issues with mine; it was never reliable, so I had to replace it. The front derailleur is attached to the bottom bracket; removing it will be a major pain in the arse, so I don't recommend doing that if you're a novice. I replaced mine with a Deore that attaches to the seat tube, something that's probably overkill for you. If yours is still working I say keep it; just be aware that it gets bent out of shape very easily.
It's probably a much better idea to replace the rear shifter and then examine if the RD is still working. My RD started becomming detuned around 500 miles or so and it got progressively worse and inaccurate. You may want to replace that with an Alivio RD, shouldn't be too expensive. Much easier to replace than the FD. But again, yours may still work fine and it's the shifter that's the problem.
If you want to get a rear rack for utility purposes, be aware that you'll probably need to find some longer rack brackets; the GT Triple Triangle design means that the seat stays are at a much lower angle than most 26" bikes, and therefore the default brackets racks come with are usually way too small to let the rack maintain a level position. I had to buy a pair at my local bike shop (which they had lying around in a spare parts bin); wasn't able to find any online.
As far as a saddle... I bought a Brooks. $100... might be out of your price range. But oh my lord it is so worth it.
Tires... I bought some Schwalbe Marathon Supremes. About $50 a tire; 26x2.0. I love them; they're strong and you can run over things like glass without worrying too much (still try to avoid it though). They're slick and fast as well. If you want cheaper tires, I had some WTB Slickasauruses on for a year. About $20 each. Very slick 26x1.5's, fast, but you have to be more careful about what you ride over. If you go with those make sure you stock up at home with plenty of spare tubes.
PS: If you ride a bicycle, you're a cyclist

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