You almost certainly do not need buried or micro vias on your first 4 layer board!
Buried vias are vias drilled between some inner layers only, and are an extra process step, on a 4 layer board your inner layers are probably power and a ground plane so you don't have any buried routing layers, and even if you did, adding buried vias is not a cheap option.
Micro vias are vias having very small hole sizes, they are laser drilled and there are strict limits as to how many layers you can penetrate because of aspect ratio limits. You usually use these when trying to fan out a very fine pitch BGA or similar where there is not other way to do it, but by then you are into at least 6 or 8 layers and you will be defining the stackup with layer thicknesses to suit, it is viewed as a high density process with proportionate costs.
For a newbie four layer all vias should be simple full stack, probably minimum 0.3/0.65 or so, and personally I would not tent (Vias make good test points) unless house style calls for it. Vias should not in general have thermal relief (IIRC you need to set a polygon connect rule to make this happen).
Regards, Dan.