hi we have just started growing veg for us and the pigs, although we have got a lot outside in big planter boxes and a greenhouse.
i started my cucumbers off inside they grew huge but my intention was always to put them in the greenhouse to finish off, i should imagine they would grow fine indoors if you have room for them..organic ones seem to grow bigger.
peas in pods do well indoors, my mum used to keep them on our kitchen windowsil and you get a small variety so they dont grow overly big.
carrots grow well in pots ive had some small ball shaped ones from pampered piggies and the longer ones and they have grown well in pots.
cabbage will grow ok in pots aslong as you put 1-2 seeds in and seperate any little ones before they get too big as spring cabbage needs quite a lot of room to grow.
ive attempted brocolli this year, which prob can be done in pots but mine hasnt grown its in the ground and got eaten by slugs, as did the kale
all sorts of herbs, ive grown corriander and parsley which the pigs like if you go to your nearest wilkinsons you can buy some propergator things which are small but enough room to start off plants, or grow your herbs in as they have a cover it keeps the wind off etc and a chill if there is one. my mum started her rhubarb and tomatoes off in them.
there are prob lots of other things just try them and see if they grow lol