The previous post mentioned the Compac 17, which might be difficult to rig on a single-handed basis. A mast tabernacle (mast hinged above deck) is helpful in this regard.
Smaller catboats might offer a better solution. Compac makes a 14 ft daysailer, which displaces 500# (vs. 1500# for the 17). Other catboats in the 14' range include the Arey's Pond 14' at 700# and 7' beam and the Marshall Sandpiper (15.5', 7' 1" beam, 1050#). There are some older catboats in this range, such as the Minuteman and Handy Cat. The Catboat Association website list used catboats for sale.
The catboat rig is pretty simple and the centerboard arrangement lets you get into skinny water. You can nose these boats up to a beach, but I'd leave them floating in 1' ft of water anchored fore and aft and walk ashore. The weight of these boats, including trailer and gear should be well within your car's limits. The real advantage of the catboat is the form stability and the relatively benign sailing characteristics. Catboats are famous for weather helm--hence the large "barn door" rudder. With weather helm, you are likely to head up in a puff, rather than heel way over.
The downside to the catboats is their initial cost--especially new. The upside is that catboats are in a cult boat category and their resale remains high. They are typically very well built for their size and age very gracefully. Check the Catboat Association site for clues on used asking prices.