My preference lies with (in Norwegian) steinsopp, brunn- and rødskrubb, as well as piggsopp and kantarelle - (sorry, don't know their English names: Google translate suggests boletus, brown scrub, leccinum versipelle for the first three)
Certainly those are good species. I would add some more, my fancy for mushrooms is getting the better of me.
Italians are mushroom-mad, the authorities have had to put firm restrictions on how much one is allowed to pick, or else several good species would be eradicated completely.
Anglo-saxons have always been primitive regarding mushrooms, so their names for them are a sorry, inadequate, despicable little vocabulary also. They tend to call the edible species "mushrooms" and the inedible and poisonous ones "toadstools" and leave it at that. (Funny thing, did anyone ever see a toad/frog sitting on a mushroom, or how did it get that name?) But anyway:
Among the "boletus", the types with something like sponge with pores opening on the underside of the hat (rørsopp), there are also
smørsopp (butter mushroom);
lerkesopp (larch mushroom, grows only under larch trees, since they are in symbiosis with larch trees);
sandsopp (sand mushroom) - which has orange-yellow "meat" which turns a vivid ink blue when you cut it and it is exposed to air;
fløyelsrørsopp (velvet sponge mushroom), and a few more.
Among the "gill mushrooms", the types with sort of sections under the hat, from the stem outwards (skivesopp):
the best of all I hold to be ekte riske (genuine riske (whatever "riske" can be translated as)). It is yellow, with green rings and a dip at the centre of the hat, grows rather deep in grass meadows, not so much in forests, delightful nut-like taste, the only trouble is that maggots and worms like them as well as we do, so they are usually worm-eaten;
rimsopp (white frost mushroom), beige-yellow, with a ring under the hat and sort of shiny shells over the ring, beige gills;
then there is vanlig sleipsopp (common sticky mushroom) which has a brown/darkish hat, often with darker spots which make it look rotten, grey gills rather far apart under the hat, lemon-coloured "socks" at the bottom of the stem. The "sticky" part of its name stems from a sort of sticky "veil", which prevents flies from getting at it and laying eggs. So it is almost always completely clean and nice. The lemon-yellow sock makes it uniquely identifiable, no danger of mistaking something poisonous for vanlig sleipsopp. Yum yum;
honningsopp (honey mushroom) grows on rotting wood. It used to be quite popular and it tastes good, but some years ago the botanists found that it does contain a poison which slowly nibbles at your liver!, so there is now a warning out in "mushroom circles" against it;
then there is frostsopp - no, I think the proper name is frostvokssopp (frost wax mushroom, grows very late in the autumn), of different colours;
blåmusseron (blue mushroom, also late, electric blue colour), grows on fermenting rubbish dumps, you can take some soil on which it grows home with you, and if you are lucky, the "roots" (mycel) will manage to grow again, so you can grow it in your garden if you take care to give it some wet, rotten leaves.
And of course all the kremle types, some are more or less poisonous, but not terribly to, and you can test it by tasting a little bite, if it is unpleasant, then you spit it out and throw the mushroom away, if it tastes good, then it IS good.
Actually, the disreputable "fly agaric" family, whose members include deadly poisonous green, brown, yellow and white fly agaric species (in addition to the very well known red one, with white spots - it is poisonous, but not usually deadly, I believe one vomits and it doesn't exactly improve your intestines, kidneys and liver - the vikings were reputed to eat red fly agaric to make them angry-wild and combative, it sounds very unpleasant) - - but anyway, that family also has some species which are edible and very good: ringløs fluesopp (ring-less fly agaric, no ring under the hat, different colours), and then rødnende fluesopp (blushing fly agaric), whose meat turns rose-coloured, but take care not to confuse it with the brown species.
Actually, I saw a kind of landscape exhibition once in France, with green fly agaric thrown in, growing in moss. The guide who commented on the exhibition said that e.g. in Greece green fly agaric can be eaten, because the weather is so dry that the mushroom does not have the necessary moisture to develop the poison. - I wouldn't like to try it out.
This excursion is getting far away from Russia, I am afraid. But mushrooms can be a passion.