I was recommended Lovat's
vat registration online service. Very convenient service, all the steps are clearly explained and the process is fast. The prices are quite reasonable, especially considering the level of service. The website has a transparent pricing plan, you can choose what suits your needs. I didn't look for cheaper options as this site was recommended to me by my colleagues. The timeline depends on the country you are registering in. But in general, the process takes anywhere from a few days to a couple weeks. I got a response and all the necessary steps within a week.