If I remember, you have an LX. Can't remember if its auto or manual though. For the purpose of the textual diarrhea that follows, I'll assume you have a manual.
If all your gears were sluggish, then I'd go looking for problems. But I think this issue is much simpler...
I don't believe in such a thing as a single sluggish gear, unless the gear is damaged. I do believe that engines run most efficiently in narrow rpm ranges and I think this is your problem. I notice hesitation in 2nd gear of my 91 LX manual, but only in the < 2000 rpm range. I'm sure people would notice sluggish performance in any gear in this rpm range, but 1st and 2nd are the only gears where you might spend time here. Simply upshift quickly from 1st to 2nd when your rpms are at least 3500 rpm in first and the problem should away. Unless you upshift at really low rpms in the other gears, you never see <2000 rpm in third, fourth or fifth (unless you change gears really slowly).
Try it and then get back to me about how it works.
As for the pulley, I also don't know which one you're talking about (I assume its an accessory driven off the serp belt, not the timing belt), in which case you may simply have a loose pulley bolt.
If your car's got more than 150,000 km or so, there's no way you're still on the original timing belt. You should change the timing belt every 100,000 km. Fortunately, the LX is not an interference engine, so if you believe in the "fix when broken" philosophy, you'll do no damage. However, you're at the mercy of Lady Luck...if you're really unlucky, it'll break in Hamilton or Windsor.