The outfits that I know are highly efficient - you can get such a 'tree' of 3 companies (for the 'Cyprus route', a reasonably well-known construct) including registration fees, rental of po box (you don't a physical presence in all countries you're registered in) for 5000 euros (excluding any share capital you may have to put up upfront). Not something you'd do on the first day of incorporation, but hopefully after a year this amount of money shouldn't be a problem any more. Don't try to organize all of this yourself - pay the intermediary a bit, they have offices across the EU with specialists who do this every day. You need someone who will provide you with exactly one point of contact that takes all the work out of your hands.

Re: 'just pay your accountant or lawyer', not to pounce on you but this is incredibly naive. Accountants and lawyers who spend 95% of their time doing mundane things like the books of the carpenter down the road are not qualified for this type of work. Any high-tech company owes it to itself to find highly specialized professionals, who will pay themselves back manyfold, even if you think they're expensive. (heck they are expensive. most charge 150 euro and hour or more, plus office overhead). Still when you're a real company (i.e. not doing 10k a year in iFart apps) it can be money well spent.