We used budget also, as it is very close to port.
I booked on costco.com, gives you a bit of a discount over budget.com.
AAA should also have lower car rates, if you book with them.
When booking, remember rental car prices jump around even more than airline prices do. So book, but check every once in a while, sign up for the special alert emails and you may even come up with a better deal. As always, if a better deal does show up..be aware of the original cancel policy, and book the new deal first, then cancel the old deal if you are within your cancel policy from the first deal.
You should be able to do this all on the internet.
We went on the recent 14 night out to CA..so we needed a one way rental from the house to port. Budget was so easy and the people were so nice. Drop off was a little crazy, hubby dropped me and the luggage and the port and went back to budget to drop off car and ride budget shuttle back to port. Well, a number of people..ugh, for whatever reason took their entire family with them, and all their luggage to budget to drop off car..so entire families/luggage were filling up van. So, definately drop you family/luggage at port first. I was able to go get hubby and i both checked in, get in line to board and all he had to do was join me when he got back. I had his passport, he had his DL for id. We were good to go, very easy. The rest of those people that didn't drop someone at port first were in a very long line.