What type of yarn would I use to crochet a purse?

Any kind of yarn. Whatever you like. The brands don't matter very much.

My daughter has made several bags recently and she used Red Heart Super Saver yarn because that is what is most easily available in our locale. That said, the yarn used for your purse could depend on your pattern and the use to which you intend to put the purse. If you want to use it as a purse, holding objects of various size that might fall through holes, you might want to consider lining it with cloth. If you are going to use it as a project bag, you can still line up if you want to, but you might be able to get away with using a tight, close knit stitch, like single crochet with perhaps a hook a size or two smaller than called for in the yarn. Yarn won't fall through but needles and hooks might if the holes are too large. If you are wanting a grocery bag or bag to hold fruit and such then even an open weave would work and you could use chunky yarn or even rope for that sort of thing. I obviously haven't used all yarns available on the market, but of those I've used I have found Caron Natura a good yarn for afghans and I would think for purses as well. It seems to be a sturdy yarn, slightly stiff when crocheting though not as stiff as Red Heart, but washes up nicely. Lion Brand Vanna's Choice is a favorite of mine as well. Bernat has some nice yarns too. I probably wouldn't use Red Heart Soft, Bernat Satin, or Caron Simply Soft yarns because they are thinner than the other worsteds and though soft, soft is not really what you're looking for in a purse. But that is just me. Another thought is if you want to felt the purse, you wouldn't need to line it. Then you would want to use a wool yarn. Hobby Lobby I Love This Wool is a nice wool yarn. Lion Brand also have a few wool yarns as do most manufacturers. Wool Ease will felt but might take longer as it is not 100% wool. Cotton yarn might also be considered as it might be able to take more weight without stretching than acrylic. It does seem to create a heavier finished project. That may or may not make a difference. Chunky yarn will work up faster and can do fine if you use a close knit stitch.

As I told you yesterday it doesn't matter. Any reputable brand that you are able to buy easily will do the same job. As for colour I would chose a darker colour because bags do get dirty, especially the handle, so need to washed frequently. Pale colours soon start to look nasty.