Now, I would never recommend a small or mini sewing machine, as I have 7 machines all of which get used daily. None of them were less than $600.00 when purchased. However, a friend of mine bought a mini Janome for scrapbooking. I'ts a lightweight machine that is just perfect for this application. It handles cardstock beautifully, has basic stitches that I see you using in your cards and I think it would be a great choice for your card designing. I've use the machine and think its perfect for what you are looking for. It does sew fabrics, but nothing heavy or thick. an important feature of this very inexpensive machine is the top loading bobbin. Most inexpensive machines don't have this feature. Don't by a cheap wal-mart machine....you'll regret it. Check out these videos on youtube for the machine.
Like I said, I don't recommend mini machines, but I have 3 Janomes and love them all. This Janome mini is not really a MINI, but a small scale, lightweight machine put out by a good company. You can find it on ebay, amazon, on line:
Heres some comments on it by scrappers: