Have you checked at 3DHubs.com for printing services in your country? My guess is that it's better served than you might think. Have you actually done any 3D printing yourself? The time and expense involved in operating and maintaining these machines shouldn't be underestimated. I'd suggest getting a small, cheap machine and experimenting with it, before plunging in with both feet. Your budget is enough to buy a few machines, but if it also has to support the business as it gets going, it's not a lot of capital to burn.

As for your questions:

1. Should my company be from the start a 3D service business or I should make products that I can sell due to my business connections?

[If you think you can sell things you can design and print for a reasonable profit, then sure - go for it. That's likely to be more lucrative than printing things for other people, which is a low-margin business, considering that someone who wants to do that can easily buy a machine for themselves for a few hundred dollars, or whatever you use for money there.]

2. If your answer is to make products, what products you would make?

[Products that would sell for twice or more what it cost to make them, factoring in amortization of your machinery, overhead, maintenance, labor, and materials.]

3. Would you buy one or more 3D printers for 10.000$?

[That would depend on what I was trying to make. That's not enough money for a machine that prints directly in metal, but it might be enough for one that sinters plastic powder into parts that don't need supports. On the other hand, you could buy a flock of cheap machines, if they are good enough to produce the products you're selling.]

4. What is the 3D printer(s) you would recommend and what are the applications?

[See the answer to question #3.]