Sorry, have to split blackberries and raspberries into two distinct groups, as they require very different culture here (zone 3). What are Juneberries... are they saskatoons? If so, they ripen July in my climate, so Julyberries :)

Raspberries - 5FE

Blackberries - 5FH (blackberries need to be really soft to develop peak flavour and can't be shipped that way, so in my zone it's grow your own with serious winter protection, or buy the often sour, hard kinds available in stores).

Blackcurrants -- haven't tried enough to rate, currant worms are a big proboem here.

Haskap - 2FM - Too sour for my liking when I grew them myself, though I have had okay ones given to me. I ripped my plants out. I rated them M instead of E only because I had trouble getting a good fruit set.

Blueberries - 5FH -- I haven't actually grown them, but I do like them, and I rated them H because our soils here are naturally high pH, also for winter hardiness issues in zone 3.

Gooseberries -- 5FH -- I love fresh red gooseberries, but currant-worms are a huge issue here, thus the H rating. I grew them years ago but pulled them after total defoliation from currant worms. Thinking of trying them again but wrapping them from leaf-out to harvest.

Juneberries... if these are saskatoons, then 5FE.