One thing to do with a Spitfire is to check "crankshaft thrust". This can be an issue with the Spitfire engine (indeed, ALL Triumph engines, including TR6, GT6 etc). Fortunately, it's not an expensive or complicated job to deal with.
To get an idea of the crank thrust, park the car in neutral, engine OFF (use wheel chocks to prevent it from rolling). Grab the front crankshaft pulley and pull it forward and backward. There should be almost NO noticable "play". The maximum play (or "thrust") is about 0.012" (or about 3 or 4 thicknesses of normal paper).
If you feel that there is noticable play, you may need to buy or borrow a dial gage and investigate further. Check some of the Triumph forums and search for "thrust washers".
As I say, the repair is fairly simple and, will add many miles of life to your engine (but if you ignore it, the damage can be very serious).
The 1300 engine is generally considered the best. The newer, long stoke 1500 is sort of a dog (although I've have one in my racer for the last 50+ race weekends
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Also, front suspension trunions/bushing can wear out....look for looseness.
And, the u-joints and bearings on the rear halfhafts (axles) often are worn. Be sure diff mounting bolts are OK. And inspect the single rear leaf spring for cracks.
All Brit cars have rust issues, but the Spit has a separate frame, so it may be easier to repair than a uni-body.
Some folks prefer the newer single-rail trans....but that's what I have in my race car and I've killed two already.