I like to sew on cards but agree that the mini machines are a total waste of money. I also can't imagine pulling out the big machine.
When I sew on cards I'll use a ruler and make little pencil dots everywhere a stitch will go in or out. Then I use my paper piercer to make a hole at each dot. Then I sew. I've found that if I just try to pierce the paper with the needle it gets messed up and nothing is straight. It also helps to put a little piece of cork board behind the paper when piercing. You don't have to push very hard and can control the size of your hole depending on whether you are sewing with thread, yard, or twine.
I hope this helps. The money you save on a useless mini machine could be used toward the other supplies you may need.