you can use an 02j box (1.8t box) but this woud mean fitting an 02j shifter (which you will have if you have the mk4), the reason people use the 02a is the 02j box's generally dont have very good ratios for the mk3. someone with the same engine and an 02a box will feel like a faster car. the 02j shifter is the better shifter though, it gives smoother gear changes and is generally a better design
you should check out
www.clubgti.com they have a dedicated 1.8t section in their engine section and it has a lot of info plus very knowegable people to answer questions
(nothing against anyone here! a lot of the ppl here are on there as well:P)
One thing you will need to do is get your mk3 loom modified together with the mk4 loom like madmanmart says, there are people who will do this for a fee, or there is a guide on clubgti if you fancy having a go at it yourself or just seeing whats involved, its a guide for the mk2 but the mk3 uses the same ce2 fusebox so its all pretty much the same
yo will also need some other bits and pieces, the standard 8v exhaust will be too restricting for a 1.8t, the standard cat wont last 2 seconds either and will also be very restricting so advise getting a mk4 cat or a sports cat (I used a universal hoffman sports car for £100) also will need a custom downpipe, qpeng do one for £200 (!) or you can get one made up, if you go down that route you could also get a custom exhaust with cat done so it all fits properly and you wont have headaches later on
there will be a million things you either forget or didnt think of when you come round to doing the work so best advise I can give is do a lot of research and triple check everything is ready before you start work