Most Blackberries are floricane fruiting, meaning they bare fruit on the 2nd year of cane growth, meaning if you planted them now you would get your first crop in the summer of 2017, there are also some Primocane fruiting blackberries which fruit on the top half of the cane the first year and on the bottom half the second year, first crop would be in August or Sept 2016, the next crop would be in about May of 2017, then in Sept again with next springs fresh canes.

You may be getting a late start planting, I am not sure about your location, but I planted mine in Feb in 8b/9a in Louisiana when we were still getting occasional nights with light frost.

If you are looking at a Primocane blackberry I would suggest Prime Ark Traveler (not to be confused with the other Prime-Ark series, Jim, Jan, 45, or Freedom). I bought mine as bare roots from Simmons Plant Farm in Arkansas, they had the best price by far that I found online. These are growing at nearly twice the rate of any of the 3 varieties of blackberries I planted this year (all others are Floricane 2nd year fruiting). Just note the primocane crops tend to fail in HOT summer conditions, so if you typically have summers with highs above 90 degrees expect limited first year production, on a positive note they tend to have heavy second year fruiting if they have a light first year.

Blueberries by contrast put up canes that yield berries for multiple years (some things I have read say a 6 year productive life for a cane before they should be pruned), howver may again be getting a late start planting, and unless you have very acidic soil, you may be too late as most recomendations are to spend 6 months to a year acidifying soil for blueberry planting, they like a pH between 4.5 and 5.5. I just planted 4 more today myself which is about 6 weeks late for my location, but it was on a whim and my native soil runs between 5.5 and 6.0 for pH so only needed a small tweak. Like most fruit both blackberries and blueberries have chill hour requirements so check your chill hours before selecting blueberries.

p.s most blueberries start fruiting in the 2nd year, however most plants you can buy are 2nd year plants so you may get fruit the first year if you can get them in the ground before they bloom (all of mine finished blooming last week), most newer releases are semi-self fertile, but get better crops if the cross pollinate with a different variety that share the same bloom time. I also bought the pink lemonade blueberrries that I planted today from Simmons, my thought is the more stuff I buy from the same nursery the less chance of my plants picking up a virus. Quality of the blueberries I just planted might be a little lower than some I have seen in local garden centers, but the price was 1/3 as much and I am sure they will perk up by next year.

You might want to read up on honeyberries as they take part sun/shade conditions and bear blueberry type of fruit.