My 2 cents
If you want to beggin flying for cheap, look for used rtf airplanes on ebay. I know someone who sold one sig kadet 40 rtf for $200. But be careful, soemtimes you can buy something that is not airworthy.
II think you can fly at the beach, but not till you become a somewhat experienced flyer, and event then, with small electrics (30-40 inches wingspan) and slow. Check out the collection of depron airplanes, such as foamie factory. The problem with the beach is its usually gusty.
Sailplanes are another option.
But these are for later. I'd reccomend to find a flying club with a grass or asphalt runway and an instructor. It will help you much. I'd leave what I mentioned above intil you are solo for about 2 months.
As for a trainer, try the sig kadet. Its the best trainer I've seen. The airplane itself costs $140, $40 for an os 40 la engine and then there's the radio
you have a couple of choices here. all of these usually come with servos and a receiver, so you can put these into the airplane
1. A cheap $200 radio, such as the hitec 4 channel. I believe they call it an eclipse. It will fly your airplanes very well, but you can only have set-ups for one airplane per radio
2 an $400-1000 programmable. These cost a lot, but they have memory for a lot of airplanes and are better in the long run

You can get good deals on these on e-bay but BE CAREFUL! And whatever radio you have and whatever set up you have, always range check your radio gear
That's it for now