Looking at this page in 2003, I would probably add some sailplanes now, recommending slope flying as a lower-stress beginner's approach then electric flying. Think Zagi 3C, Boomerang, Combatwings - all a bit twitchy as flying wings, but totally bounceable and easy to repair when nececessary. Also look at the free simulators to get the reflexes right cheaply: CRRCSim, Slope Soaring Sim (put these names into google.) Still, the electric planes listed here remain good options.
A beginner's plane should be cheap, easy to fly, able to survive crashes, and repairable. Some options are:
These planes are all foamies, built from foam, and good for parkflying. They can deal with a little wind. Many other parkflyers exist that are foamies but more fragile, or that are wood construction, and have to be built from kits.
Another interesting looking plane is the Mugi, which has to be scratch-built, but it looks simple, and it's cheap.
Someone who already has RC flight experience can act as an instructor. An instructor can explain the basics, can take the controls to save the plane when it gets hairy, and can offer encoragement and advice. Sandy Stone is my instructor.
Before flying and crashing actual planes, it helps to use a simulator on a PC. Several simulators exist. I used Realflight G2, which is pretty, realistic, and expensive. It does not offer many electric planes, but the reflexes that one learns are transferrable anyways - that is what counts. Before Realflight, I also used FMS, a free simulator. It is much simpler, but works too. Also popular with electric fliers are the newer Cockpitmaster simulators that offer many electric planes, don't look quite as good as Realflight G2, but are much cheaper. Other simulators exist. It is possible to connect one's transmitter to the PC, to use it in a simulator, for a realistic training experience. The commercial packages offer cables to do this connection, the free one's offer instructions to build such cables. It is good to have a name-brand radio (Hitec, Futaba, JR, Airtronics are some popular brands in the US) - some cheap radios, and some old one's don't work with "trainer cords". I have a Hitec Flash 5X radio, which is not their cheapest, but still relatively cheap, and very flexible.
Besides parkflying, one can also learn to fly in an RC club with an airfield, the traditional way. Several clubs exist around Austin, listed on the Cedar Park Hobbies site. The clubs around here tend to focus on "gas" planes (really they don't fly with actual gas, but they do have glow (combustion) engines, not electric motors.) One can join such a club and find an instructor there who will teach flying on a glow trainer airplane. Glow planes generally have more power, and are alot louder then electic planes, confining flying to the club site. A lot of fun too, but a different deal then electic flight. Glow planes and electric park flyers don't mix too well, because the slower, cheaper electic planes can get in the way of the glow planes, but the clubs usually still allow electic planes, and some club members fly them, too.
Flying on a club field requires that one has AMA membership. The "Academy of Model Aeronautics" membership comes with an insurance for RC pilots, and with a set of rules. AMA mambership is a good idea in general. AMA rules are common-sense rules, and good in the park too.
Another, different way of flying is offered by sailplanes and gliders. There are hand lauch gliders, which are simply tossed in the air to search for thermals, there are hi-start sailplanes, which are lauched with a bungee cord, and there are sailplanes that are launched by a powerful winch. A variation is slope soaring, in which one flies sailplanes in the lift generated by the wind blowing up a slope, instead of using thermals. Central texas does not offer many good slope soaring sites. A variation of sailplanes are powered gliders, which are equipped with an electric motor, either just to gain altitude for thermalling, or just for fun. A group of people in Austin does fly sailplanes, often meeting in Georgetown, across the field from the club site there. Some sailplanes are can be can be flown in parks.
The best Austin area hobby store is Cedar Park Hobbies. Austin also has two Hobbytown stores, which offer a smaller selection of goods, but a shorter drive. Many online stores exist. Hobby People and Hobby Lobby are two big one's. If possible, supporting a local store is a good idea, but many electric flight items are hard to find locally. A very active electric flight site is the Ezone. It offers a lot of good contents, including a large, active discussion board. The ezone has commercial sponsors. Many small airplane maufacturers have sites. Finally, a good print magazine to read is Quiet Flyer, available in Austin at Bookpeople and in the hobby stores.