I don't think that even with a greenhouse berries would make a good candidate for indoor growing, but you can literally find a berry plant for pretty much any climate zone, so outdoors is easy. Raspberries will dominate your entire world so make sure you have lots of space or plan on cutting them back frequently. Strawberries are easy and don't take up much room, but yield is low unless you have a lot of plants.
There are many disease resistant varieties and bird netting will solve the bird problem. Find someone who has a blackberry or raspberry bush and ask them for a cutting, couldn't be easier. There are much harder food crops to grow than berries and many people grow them, seriously, not a big deal, give it a shot.