There are great info sources on the web to help you learn what to purchase if you want jam from your garden. Many folks do not realize that all berries do not have identical growing/fruiting patterns.
The primocane (sometimes called fall bearing or everbearing) varieties are the least amount of work in the long run IMO. Primocane is the term used to describe a berry that will begin growing in the spring and have a crop of berries by late summer/early fall and usually fruit til hard frost. Primocane raspberries have been around for many years. One of the most widely available is the Heritage red raspberry. It is delicious and very productive in most areas. Newer varieties have slightly different characteristics regarding firmness, shape, flavor, and season length. I have five or so varieties, and currently my fave is Jacklyn-a firm, pointy and tasty morsel that is outstanding on small tarts and makes great jam. The primocane reds seem less thorny than summer bearing types. The easiest aspect of the primocanes is the maintenance. In Dec, cut down all the canes and discard. In the spring, at least by the end of April in zone 6, thin plants so there are only four per square foot. 6" spacing in all directions gives optimal growth. Those you pull can have leaves stripped and dried for teas. If you desire to expand your patch, carefully dig new plants with roots attached and transplant. These berries love to be fed, weeded and mulched. For heavy production in a windy site, I use a two line trellis on steel posts running parallel 33" apart in a 50' row. I also prune any growth over 48" to encourage side branching and increased fruit production.
Summer bearing raspberries are more complex in care IMO. Check web.
The primocane blackberry I have is Prime Jan. It is very THORNY! I am trying to give it all away. I raise it as for the red razz. I have to use pliers to hold the canes aside to gather the very tasty fruits. The thornless blackberry I have grows rampant, is not primocane, but does not produce much, despite pampering.
For any of these berries, I suggest you get at least three plants to start. As time and space allow, you will be donating excess.
Ask on freecycle , join a gardening club, or place ads at the coop...you may be able to find thinnings from a local gardener or two who will share their excess with you. Good luck!