Renting will be way too expensive for you. It's best to buy a good used one and sell it upon return. Or...you might really like it and just keep it for other trips!
As stated, Jan - March are not good months for travel. You'll be hitting a LOT of rain and cold weather. The rainy season starts in October/November - earlier in some places north. Good weather for the coastline above San Francisco would begin in May, possibly April in some places.
I would suggest you start from Houston in April and head to San Diego and upward finishing your trip mid-June or else do a summer trip or leave Houston in August and return mid-October.