Conner,
Starter is pretty easy to remove - just 2 x 9/16 inch bolts. Just "bend over" the
the fender for the top one and crawl underneath for the bottom one. It can be pulled straight forward to in front of distributor, pointed down, and then pulled up. It's easiest just to remove the distributor and pull the battery out. But it's easy to remove.
Fix or Replace - You might find is cost efficient to just buy a new one from Moss Motors or Victoria British if yours is not working correctly. Sprite/Midget or MGA - all use the same starter. New for around $130 maybe a little more. VB part # is 8-155 for quite a few BMC products. I have one in LipStick, the column shift '65.
Moss Motors -
http://www.mossmotors.com/Shop/ViewProd ... exID=32991
Victoria British -
http://www.victoriabritish.com/icatalog ... x?Page=144
If you go the repair route, I have found from a couple of local places the starting cost is $55 to look at it (beyond the quick bench test of it works/doesn't work). From here you can start adding on the cost of individual parts, plus cleaning the rotor and armature, turning the commutator down (if needed), new bearings, etc............ oh, and if the shop can find the parts for a Datsun starter, which they probably cannot and they will have no idea that parts from a BMC starter will work - all available from VB or MM.
If you simply need new drive teeth, you can do this. Just pull the 1/8 cotter pin and remove the drive assembly, replace drive gear, and put back together the same way it came off. This is about ~$50 worth of parts. All available from VB or MM.
Course if you have some extra cash the gear reduction starter will also work and it sounds pretty cool when you start the engine. From VB you want part # 10-550
http://www.victoriabritish.com/icatalog ... x?Page=176
Hope that helps
Andy