Unless you have a lot of money, and/or don't like the way in which your estate would be distributed under state law, you don't need a will. If you have a will, it has to be probated at your death, and that costs a fat chunk of whatever you were passing on, and it can take forever. Get the Nolo Press book on Wills and Trusts before you spend money on an attorney. Nolo Press is an invaluable resource. They publish handbooks on the law for non-lawyers, and they can save you BIG bucks. They're located on 9th and Parker Streets in Berkeley.
You can't actually decide who will raise your child if you die or are incapacitated. The court makes the ultimate decision. What you can do, and should do, to have some peace of mind, is to write out your wishes under the title "Nomination of Guardian for Minor." You can either name the person or persons you would want to become your daughter's guardian, or you can designate certain people, family and/or friends, whom you would want to make the decision as to who would be the best person to be nominated as guardian, given the circumstances at the time. (This kind of provision helps cover the situation where the person you nominated as the prospective guardian is, for some reason, unable to do it at the time.)Again, the court doesn't have to follow the recommendation, but it gives it a lot more weight. Put this document with your important papers.
You might also want to pick up a Nolo book on family law, because even though your daughter's biological father has never seen her, or cared for her, he still has parental rights simply by virtue of having fathered her. You may want to get him to give up his rights so your present partner can adopt your daughter.
The other thing you may want to do is marry your present partner. There is no "common law marriage" in California, and if he dies, you won't get any social security assistance to help you raise your younger daughter. If you marry him, and he adopts your older girl, then if he dies, you will receive social security for each child, and, believe me, it makes a big difference.