This link will give you a bit of an insight in pre purchase and covers both the Cooper and S (with the exception of the Super Charger on the S model). https://www.youtube.com/watch?v=QUhzyfb3cxg
Do a search on here for what to look for on purchasing a Gen1 Mini as it has been covered often.
If you can obtain the VIN #, see if a BMW (Mini) dealer can pull the cars history for you (wont cover any 3rd party work done on the car).
Common issues if its a manual will be power steering pump, leaks around the thermostat, worn suspension bushing. Do you know someone (friend or family) that is familiar with the BMW-Mini to inspect it for you.
I wouldn't be to concerned about Chilli or Pepper, I would be more concerned about the cars condition in regards to road worthiness and any obvious signs of crash repair odd tyre wear etc.
Place a magnet against the body work to see if it sticks (use a hanky so between the magnet and the paint so you don't scratch it), if it doesn't, its full of body filler from a previous repair.
Have a contingency plan for future repairs and hopefully someone who can help mechanically as any dealership will be expensive.
You state your daughter does not currently have a license, if your looking at a Cooper S, I would recommend looking else where and consider a Cooper. A Cooper S is a powerful car for a first time driver and may not be the wisest choice as a first car.
The following is from previous posts I have commented on and hopefully it will help you.
Pull the bottom of both rubber door seals and the rubber seal at the bottom of the tailgate and look for rust.
Check to see if signs of water in the Battery well (cooper S).
Check for leaks around thermostat.
Check coolant, should be blueish (Dependant on Country) and not just water.
Check PS Fluid, should be a watery green.
Look at the belt tensioner with engine running, if its bouncing around, needs replacement.
Check the Belt for splits etc.
GET UNDER THE CAR (don't care if its a dealership or private buy)
Look for weeping clutch slave cylinder.
Look for oil leaks from a small slot at the bottom of the gearbox where it meets the sump (rear main oil seal leak ?)
Look for oil leaks at the belt side of the sump (front main oil seal).
Shine a torch up around the exhaust manifold and look for oil leaks on the right hand side of the vehicle (leaking Oil Filter housing)
Shine a torch around the Power Steering pump for leaking hoses or steering rack.
Pull the wheels at 9-3 and 12-6 for wheel bearings for tie rod ends and ball joints.
Use a small crowbar or large flat blade screw driver, ever and check the control arm bushing isn't shot.
Look at all engine mounts (where you can, gently pry with a ever to check for splits in the rubber).
Inspect all brake pads.
Open oil filler to rocker cover and look for grunge or milky white oil deposits (leaking head gasket).
Check all hoses.
Check for an oil leak left of centre at the front of the engine (its a 30cent Crank Case Sensor O-Ring and easy to fix) often mistaken for a leaking sump gasket.
Check all lights and fittings are working.
Does the clutch or brake pedal feel spongy ?
Does it change gears OK on a test dive.
Is there a rattle on cold startup ? (timing chain tensioner and or worn timing chain guides).
Are there any chips in the windscreen.
Make sure you have the Jack, Wheel Wrench, Compressor, The Wheel nut Key for the lock nuts.
Check the air filter to see how dirty it is, will indicate if its having a regular service.
Start the car cold and look for puffs of white or black smoke from the exhaust tip (get a mate to watch).
If the car has been warmed up prior to your inspection/arrival, let it cool down ! then restart it.
Do not be scared of getting under the car either, if your not allowed, then ask why or walk away !
Expect to take 1 hour to do a good inspection before you start talking money !
That should give you a good idea of what to look for and any issues you find can be used as a bargaining tool to reduce the price if faults are found.
If it has a 5 speed box, its a Rover midlands unit and has a poor reputation but rebuild kits are easy to obtain as are rebuilt gearboxes, If you do buy, replace the gearbox oil as a priority regardless of the gearbox.
Older models had issues with the PS Pump. If its not already been sorted, you can replace with new or reconditioned units and it takes about 1 hour to swap out and bleed the Power Steering.
If they have been neglected or abused, they can be very expensive to fix unless you do your own repairs and shop around for parts.
If you maintain and look after any issues as soon as they arise, the car can be reliable but they are not a run of the mill car and require TLC.
Very few cars are as enjoyable to drive regardless of its short comings, your either a Mini enthusiast or your not.
If you buy, join a Mini club for the knowledge base, possible discounts at auto stores etc and advice when things go wrong as some one has prob been there done that and may have the solution your looking for. Also purchase an Bentley Manual or a Haynes as a minimum.