I don’t know anyone who burns olive wood in a wood burner. Olive trees are slow growing, they do use the prunings in fires but as it’s a very oily wood I don’t think it’ll do your wood burner a lot of good, bit like burning pine.
The wood sold for firewood is usually oak (quercia) and beech (faggio) it’s best to get a mix because oak is slow burning but can be a devil to light. Depending on the size of your wood burner you’ll need to get the right sized wood or cut it yourself.
I don’t know what area you are in but there are legnaia all over, if you ask the locals or look on the Internet you should find one close to you.
Many big supermarkets also sell smaller, split logs, in netting bags but that’s expensive if you want any quantity.