I would say there are 3 types of bakeries in Budapest. The cheapest, they are Albanian bakeries. The middle level is the traditional Hungarian bakeries like Lipóti Pékség, PrímaPék. In the middle level there are the all of the supermarkets's offers (Manna, ABC Lidl, Aldi, Spar, Interspar). I think the quality the quite same like in Lipóti or PrímaPék. The highest level where the prices are also extremely high as well, in the artisan bakeries.
I could say if you would like to spare your money you can buy regularly in the supermarkets however you should make a try sometimes with the artisan bakeries.
Apple Pie
Homemade bread with sourdough
Cheese sticks
Cottage cheese strudel
Easter "bread" (Kalács)
Aranygaluska
Kakaós csiga
Hókifli