Get the Bentley service manual (best price I've seen is from Amazon). Follow the "1st gen Stock Issues" forum on northamericanmotoring.com
02 to 04 justa coopers have midlands 5 speed trannies if manual. 05 and 06 have a getrag 5 speed. Midlands, bad. will self destruct at some point. Cooper S has a 6 speed getrag. IIRC, slightly taller gearing on pre 05 models. great for storming the autobahn. get 15 inch wheels for stop light drag racing, ie normal stateside driving. Cooper S tranny also has a dual mass flywheel setup. Change the tranny fluid asap. It's considered a "lifetime" fluid. 07 and newer justa coopers have a 6 speed getrag.
The 1st gen Cooper S has a serpentine belt tensioner that may fail spectacularly. Aftermarket companies make a stop bar or cable catch to prevent spectacular failure. The eaton m45 blower is considered a "lifetime" part as well. Get a used spare and have it serviced.
Thermostat housing is known to leak. On early models, the coolant tank should have been replaced. use bmw/mini coolant or evans only.
All engine variants have timing chains.
Bushings should be replaced on high mileage Minis. Front LCA bushing should be inspected for sure. Front top strut mounts should be checked for tears (good time to install camber plates
but oem if you want to stay in stock class). If driven in a metro area, struts probably will be need to replaced. Check out the Mini Cooper (R50) project car that Per and Kim drove for suspension and exhaust ideas.
The faux LSD, nee F1, is only available on the 08+ JCW.
I have been driving my daughter in my Mini since she was seven months old. luckily, she transitioned from the carrier to a forward facing child seat.
Motor on!