First welcome to the hobby of woodturning and you have started correctly by getting some tuition.
As stated buy the best tools and equipment that you can cheap stuff will not last as long.
Keep the bench grinder and don't worry about a wet grinder instead either buy or make some jigs. When sharpening a gentle touch is required otherwise you will soon grind away the tools.
Abrasives I buy some from
toolstation which are these ones I find them very good get a good selection of grits
The club member you spoke to was not very helpful. And should have at least suggest something to you.
Please note that the club you spoke to are probably just members of the AWGB and that is why their name appears on the AWGB site and does not reflect the true AWGB as an organisation.
You can always ask advice here but you will have to look at each reply carefully there are so many ways to do things not all are incorrect the main thing is to work safe and please remember safety gear, dust mask face shield and if possible dust extraction.
As suggested earlier try to find someone able-bodied to help with moving the lathe make sure that if mounted on a bench that it is strong enough to hold it. Remember to level the lathe along the legnth and across the width and thet the head and tailstock line up.
Last thing enjoy yourself and let someone know you are in the workshop working like your parents.