First of all, welcome!
It is perfectly natural to add a 156 jtd to your driveway - did you know some parts are shared between the coupe turbo and the 156 jtd? The engine block, for example? And there is a SMF conversion which uses the flywheel ( although this conversion is only for the 10 valve jtd, I think, the 20valve uses a Gm 6 speed gearbox).
However, to answer your specific questions;
Engines: the 156 diesel range consisted of 8 valve 1.9 jtd, 16 valve 1.9 jtd, 10 valve jtd and 20 valve jtd. All engines need the timing belts changed regularly , and it's a good idea to do the water pump too, not least since pump failure can also wreck the timing system. Some engines (1.9) have sacrificial rockers to prevent valve/ piston contact. All pretty standard stuff really. The engines are normally very reliable if oil changed and respond very well to remapping/ tuning.
Turbos seem to also generally be reliable; oil feed hose can eventually collapse/ carbon up ( hardly an Alfa specific problem) my turbo did over 150,000 miles with no issues .
Manual gearbox on 8 valve and 10 valve (2.4 sorry, no experience of auto box) is usually ok, bushes in gearbox linkage sometimes cause stiff change, but easy fix, gearstick housing can crack, giving vague selection, not quite such an easy fix, but not too difficult . 1.9 16v has a 6 speed box, all benefit from q2 diff being fitted. 2.4 20 valve uses a 6 speed GM box, not quite such a smooth box, and trickier to fit a LSD to/ find. All use a DMF, and clutches are a big job to change, particularly on the 10 and 20 valve jtd : an SMF can be retrofitted to all except the 20 valve. They all seem to cope well with moderate remaps, but an up rated clutch is a smart move IMHO, but standard ones seem fine for normal driving ( whatever that is!). There is a driveshaft issue on the 20 valve ( Gm box) to bear in mind, but a thorough test drive should highlight any problem, 10 valve however, is bulletproof!
Far as electrical kit goes, MAFs seem to be the biggest problem, but genuine Bosch types are not too pricey; not worth using cheap copies; get fiat ECU multiscan and you won't need to go to a stealer for a fault code reading/ reset.
Cruise control was only fitted ( but if missing can be retrofitted for around £100!) to facelift models (2002 onwards), not sure about heated seats.
Suspension issues; front wishbone bushes (upper and lower) need greasing properly and ball joints fail, along with antiroll bar bushes, link arms often seem to provide interesting noises...the standard spring/damper setup is ... A bit soft, definitely on the 2.4 and could do with upgrading IMHO. Oh the engine undertray is almost always missing/ broken; there is a popular alloy replacement, which doubles ( very effectively!) as a sump guard... You will need one, especially on the 2.4...cracked sumps are not uncommon; expensive secondhand.
They are cracking cars! You won't miss RWD, if your tracking is correct and the steering is a joy!
Go for it ! FYI; although the facelift cars have a more 'current' alfa design, the aerodynamics are actually better on the original shape!
Hope that helps, now you can have an all Italian driveway!