Congratulations on finding a single-group Linea!
I'm not really any sort of espresso technician, but I have a few links for you that might be of interest.
First up, if I were in your shoes, the first thing that I would do is to get very familiar with Paul Pratt's excellent
Espresso Restorations webpage, presuming that you're not already aware of it that is. Paul frequents these boards and I'm sure that he will chime in to help you out. He has a great pictorial essay on
refurbishing a 1992 EE single group Linea and a slightly less comprehensive essay on
a 2001 single group AV Linea, as well as a tonne of other relevant and interesting reading material.
If you are in the US of A, espressoparts seems to be the big parts supplier, although I'm sure that there are alternate sources and I have no idea how everyone's prices work out. What is nice about that site is that as well as having a
LM parts page, they have off-the-shelf
PID kits and
rebuild kits. Presumably there's a premium placed on the "make it easy" factor, but they might be worthwhile looking into.
Finally, I'm sure that you have read that the flowmeter in the AV machine means that you have to flush a fair bit of water through the group to heat up all of the tubing. You might like to fit the new group cap to it, which has an integrated flowmeter and solenoid that eliminates this problem. I don't think that you can fit the new group cap is only made to fit the new welded groups, but you might want to talk to Terry at espressoparts - I think that he has worked out how to do it.
Good luck,
Luca