As Smoggie indicated...
If you try to do this as you wrote it... it's going to be far outside of your budget. If on the otherhand, you didn't use the proper words for what you were asking or if you don't mind a minor change in those plans... it may be doable but just barely and you won't be using quality parts/hardware, it would only be a place to start.
First let's define FPV a little... That is short for "first person view". In other words you'd be watching what the aircraft is doing through a monitor or googles ( both are expensive ). If on the other hand you meant or are OK with just taking a movie of what the aircraft is doing, that may be closer to what you can afford since small cameras that can record aren't really all that expensive. FPV equipment that require a video camera, transmitter and receiver along with the monitor and other required equipment is pricey to say the least.
Another issue with FVP... you can't or shouldn't fly that way alone... you need a second person to watch for you, a spotter, so you don't get into trouble just watching through the monitor or goggles which restrict your vision.
As for "making a model" ... There are three directions to take and each probably end up about the same cost once you get everything you need. The simplest is just getting a RTF model... RTF stands for "ready to fly" and it has everything you need included. You would still need to assemble it but you wouldn't need to actually build it from the ground up. Then the next step is an ARF... which stands for "almost ready to fly". An ARF is a model that is already covered but the major parts need assembled and you still must purchase a radio, receiver, servos, motor and a few other minor parts. Most ARF's will have recommended parts suggested so that makes selecting them a little easier. Then there is kit or scratch building where you must get almost everything together and often require that you know which parts are needed for that size and type of aircraft.
A kit will often cost you as much if not more than an ARF model will... so they are more directed at builders that want the enjoyment of doing everything for themselves. If looking to do something like this, check out the RC-Help trainer that Tony has posted here and is available to download the plans for free from the forum "store". There is a build video that can help as well as posts from other users that have built it. The main material that it is built from is a flat foam that is available most everywhere and doesn't cost much. You'd still need to source the rest of the components but suggestions for those are also found in the threads about that airplane.
Once you decide on a direction you want to go in... You still need a lot of time to learn how to fly. You can't simply take off and land without having first learned how to fly. To learn, it's best to find another RC pilot to help but if you can't find one, there are RC flight simulator softwares that you can get that can aid in learning. A flight game is not the same as a RC flight simulator... the games has the flight simplified to make them more enjoyable a simulator tries to emulate real flight and flight conditions.
