I see you're in Lithuania, so you'll be under the EASA system. An EASA B1.1 catergory license entitles the holder to certify fixed-wing turbine aircraft.
So: if you do purchase an L-29, given it's a fixed-wing, turbine-powered aircraft with a MTOW under 5,700 kg, you should be authorised to certify the aircraft on a B1.1 license without a type rating. That being said, however, keep in mind that there are exceptions to the 5,700 kg MTOW rule, as in the case of some bizjets like the Embraer Phenom 100 which is under 5,700 kg MTOW but still requires a type-rating due to the complexity of the aircraft.
If, however, you purchased a piston-powered warbird, you would NOT be authorised to certify it with a B1.1 license. For this you'd need a B1.2 license.
Finally, also keep in mind that certain maintenance tasks, such as flight control rigging, will require an independent inspection and certification by another, suitably qualified engineer. Typically, I believe, the same engineer cannot carry out the same flight control rigging task on both sides of the aircraft (rigging ailerons, for instance). The primary task must be done by different engineers on each side of the aircraft and the independent inspection carried out by different engineers for each side, so you could rig one side and inspect the other and vice versa for the other engineer.
Hope that helps.
Cheers,
John