I have worked on dairy farms for years and have also had family cows.
I would ask dairy farmers in your area if they have a healthy low-production cow they would be willing to sell. Ideally, she already would be bred back and confirmed pregnant. It's great if you have the opportunity to milk her, especially if you'll be hand-milking. Are her teats short and tight, hard to strip? If you have a miserable time milking, you probably won't stick with it long. A cow with long, loose teats and an easygoing disposition is worth her weight in gold. Doesn't matter so much what she looks like or if she's only a 3-teat cow. Even a sub-par Holstein will pretty much drown you in milk unless you're feeding an army! The key factors are that she has the ability to get pregnant and carry a calf, and that she's easy to milk.
Another alternative is to go to a dairy auction, if there are any in your area. I don't mean a slaughter auction, but a sale where dairy farmers buy and sell cows. Sale barns in areas with a lot of dairy farms will hold these periodically, or you may see herd dispersal auctions advertised. Generally the cows have been sleeved (pregnancy checked by a vet) just prior to the sale and sometimes a summary of their DHIA records (production and udder health) will be available. Again, look for a low-production cow with nice long teats.
I would stay away from buying a heifer at the outset. You'll have to break her to milk, and you can't get an idea what a heifer's udder will be like and/or how easy she'll be to milk. Heifers are more prone to calving difficulties, too, especially delivering stillborn calves. The fact that she's a heifer is no guarantee she won't freshen in with mastitis or a blind quarter. At least with an older cow, if the seller is honest and/or you take an experienced friend with you, you'll have a good idea what her faults are, and sometimes the devil you know is better than the one you don't!
Anyway, JMO, and best wishes in becoming a cow owner!