If you are selling paintings as a business and gaining an income from so doing your income is taxable in the same way as any other trader, i.e. you pay income tax after the first approx �4500. However, you deduct from the money you make any expenses you had in running your business so painting materials, a reasonable amount for mileage if you had to travel etc. You will only have to charge VAT to your customers (which you collect on behalf of the tax man) if you are making large amounts (I think it is currently �50,000 profit a year). You can register to pay VAT optionally but this is really only of benefit to business who make not quite the �50K or are part of a group of businesses and so do it for complicated tax reasons.
If you are selling the odd painting for investment purposes, e.g. you owned it for a few years you may have to pay Capital Gains Tax for literally that, any gain you have made on the sale from how much you bought it. This again is after the threshold of �4500. Inheritance tax probably won't affect you. If you are buying you won't see any of the tax though the seller may have added VAT (e.g. if you are buying from a large auction house. )