Blackberries are extremely invasive, I tried to remove one bush 4 years ago, but its seedlings still come every year all around my berry patch. The same situation with raspberries. They are better planted in a pot if you have limited space or don't want constantly remove unwanted seedlings.

Rovada is a very productive red currant variety, it ripes after Red Lake (about 2 weeks later) and bush is smaller than Red Lake, berries are larger that Red Lake's. I also like Pink Champaigne (pink currant) - berries are sweeter. There are also black currants, they like partial shade more than red, pink and white varieties.

Gooseberries are very different is taste and size of berries and bushes. Invicta has big sour-sweet green berries with small "fuz" (kinda "furry"). I like Hinnomaki Red more despite that berries are smaller and red in color - they are great to eat when ripe and to make "emerald preserves" when berries are still green (groundhogs prefer them too). The only thing - branches are weeping. There are also varieties that are similar to blueberries in taste, color and size - Black Velvet, for example. I have Black Negus (European gooseberry variety) and it's an extremely productive huge bush, berries are good for making wine.

Any way, there are a lot of varieties of currants and gooseberries, suitable for any taste and purpose.

Warning- some regions prohibit planting and growing currants and gooseberries and many mail-order catalog companies won't send seedlings to you unless you have a permission from a state.

Thanks Yelena! Great advice. I am still going to plant blackberries, just cannot resist! Triple Crown variety.

Have you any experience with Poorman gooseberries?

No, I didn't grow Poorman. I had Captivator, bush was huge but berries were so small, I even didn't bother to pick them up!
I had Ebony King blackberry bush, it was constantly sick (I bought it from local garden show room). Even now, 4 years after I removed the bush, its seedlings come every year and they are sick! They sprout in my raspberry bed (between Kiwi Gold raspberries) but raspberry bushes are are tolerant to disease (actually, even Japanese beeatles don't like yellow raspberries and they destroy my red raspberries every year!) I should admit that berries were big and tasty.