Well ctn/asd gearbox from mk3 golf is your solution, but you will have to convert to cable box/hydro clutch or buy conversion pack from a some shop (I think they sell on vwdiesel with discount, I think I remember mail video).
I have converted this gearbox to mk1, it's great but I would buy conversion pack if I lived in USA (shippment to Europe+taxes was just too much for me). Fabricating gearbox mount is a lot of work if you have no experience.
Also 02a gearbox has wider differential so you will have to use shorter axles or find some other way to widen the track.
You will not be able to run better gears in 020 (stock) gearbox so this is your only option.
Also, TDI's rev much lower than TD's, so if you were to put TDI on your gearbox that would be even worse. Only way to put in TDI would be to get it together with a 02a gearbox.
Have a look around forum and consider again if you really want to have TDI, I have one I could take for free but still I rather bought another 1.6 engine after mine blew up
I think it's best diesel VW ever made.