My Raspberries are already forming fruit. You can still plant them but don't expect fruit this year. They are very vigorous and spread rapidly underground. You need a method to control them, prune them, etc. I can't imagine you wouldn't be able to grow them.
For favorite varieties, you might try the Fruit & Orchards forum here but I am sure if you were to search raspberries on all forums, you would find a lot of information already posted.

Highly invasive and obnoxious enough to handle that the weeds, like bedstraw and japanese honeysuckle, that may come, are difficult to get to and eliminate. I think you have to be very attentive, or plant them in an out-of-the way spot and make paths, periodically, with your mower to make reaching the berries easier.
I grow 'Fallgold' in sandy, acid soil and get two wonderful crops each year. I think the berries are too tender to be shipped to most markets and are supersweet.
Also, the color is less attractive to wildlife than red.

i got a bunch of raspberry sticks at a swap. there were three varieties. i stuck them in the ground a few years ago and they've produced berries every year. i did absolutely nothing to them. not trimming, no weeding, nothing exceot pick and eat the berries. birds do not bother the plants and they are not invasive. it sure beats the heck out of paying $4 for a small modly package of raspberries from the supermarket.

Heritage is a very good variety and easy to find. It has two crops a year, the first on old wood and the 2nd on new. There should be plenty of season left for new plants to establish themselves, you just need to keep them watered. I think they are best grown in a long narrow hedge, less than three feet wide so they are easy to pick and it is easy to remove the dead wood.