If you are looking for a spridget to buy, look at the following things:

Rust

check the sills, bottom of rear guards, boot floor, footwells, door pillars. Also check the spring hangers on the rear suspension.

Chassis

check for bent/buckled rails; those are the main front to back square sections on which the front suspension is mounted.

Floorpan

related to 2) above, check underneath the body underneath the driver and passenger seats. Any buckling behind the main crossmember is indication of a heavy shunt.

Engine/Tranny/Diff

depending on how much effort you want to make, you can take along a compression gauge and check each cylinder to see if it is keeping compression OK.

Check how well the synchros are working, whether it jumps out of 1st or reverse (in both cases, accelerate hard, back off, accelerate hard again)

Listen for any whine from the diff.

Suspension

jacking up each side, grab the front wheel and try and rock the top back and forth. Any significant rocking means check the wheel bearings. You should also look for play in the king pin. This is a moderately expensive fix. Check out Gilspeed's Guide to Inspecting your Front Suspension for more details.

Check the rear wheel for rocking as well (bearings), but also check the inside of the brake drums for oil -- the seals in the hub would need replacing. Check both front and back shocks for leaking oil.

Trim/Paint Condition.

Parts for sprites are readily available. There are lots of places in the UK that you can nearly all parts from (M&G International, Brown and Gammons, etc). There are also plenty of places in Australia (e.g. here in Victoria there are: Bugeye Barn, Exclusively Sprite and Midget, Gillspeed ) and in the US (e.g. Mini Mania, Winner's Circle, Speedwell).

Sprites are pretty reliable if well maintained. Some of the common failures are fuel pump (SU) (give it a whack and it'll work again), half shafts, electrics. I always have a spare half shaft with me.

Sprite are *great* fun to drive. As long as you choose well, you'll have a great time driving it!