If it is a standard leyland mini (71-78 ), you just need basic mineral oil as these engines trace their origins back to the 1940s. Even the most basic modern oils are now superior to most of the stuff you could buy when your car was new.
Any of the k-mart or supercheap brand oils are fine, valvoline XLD, castrol GTX - just any basic 20W-50 Mineral oil is fine. If the engine is worn and it is using oil at the rate of more than 1L per 1000-2000km you may need to go to a 25W-60 or thicker oil designed for older engines. Don't use synthetic oil, as the seals in your engine will not be used to it and could end up causing oil to leak out everywhere.
Probably a more important issue is to change the oil regularly, don't leave oil in there for more than 5000km - the engine and gearbox use the same oil (but you probably knew that already
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Black smoke means you're probably running rich (i.e. engine is getting too much fuel). Probably needs a good tune up. Also maybe check to see that the choke is fully pushed in when warm, and that your air filter is not dirty. If you've just bought the car, you will probably need to give it (or take it in for) a major service - unless you have receipts and records to show that all the fluids have been changed and it's been servicing recently, assume it hasn't and it's time to do so!
There's heaps of people on here who have repaired rust damage themselves, some with good picutres. Use the 'search' function at the top of the page to search for old topics - most of them will be in the 'mini chat' subforum.
Welcome to the joy that is mini ownership! Be sure to upload some photos of your ride for us to look at and if you go to your profile and fill in your suburb/town location then the members who are local area will be able to do things like suggesting local mechanics and specialists who can help you with your car, give you advice on where to get parts etc.
