Any time you want. If you're tilling for weed control, then till immediately and then till again in a month, because tilling will turn up weed seeds.
For raspberries, I like a variety called Heritage. If it's suitable for your area, it's a nice producer and it fruits on new canes - so every year you just cut or mow them down completely, making them very easy to care for and control. Yellow raspberries are sweeter, but - as with most raspberries - fruit on 2 year old canes, so require a bit more effort.
For both raspberries and blackberries, you can basically just plant them right in your lawn, so they rarely need any special ground cover. They easily out-compete weeds. But blueberries and strawberries should have a clean, weed-free bed. I don't have much problem with raspberry spread (the bramble will gradually expand, but not excessively) - but blackberries will shoot up canes 6-8 feet away from the source (I just pull them or cut them down - it's no big deal, just mildly annoying).
Plant in the fall, not the Spring - if possible (see below).
You'll want a soil test for blueberries, due to their acidity needs. Then you'll have to adjust the acid-content of your soil, which probably means planting in the Spring. You should start this now.
As a general idea for spacing and placement: My 3 year old blackberry bushes each take up a roughly 4-by-4-by-4 area. My 10 year old raspberries are around 3-by-3-by-3 each. My blueberries never thrived. My strawberries creep toward full-sun of their own accord. Animal thievery is most common with the strawberries.