USD 150 is tight if you want to bring a half-decent camera up. You can buy cute little quads for as little as USD16, but the firmware for these things is always closed. Same with the DJI Phantoms and their Chinese clones.

What you're looking for is a flight controller with open source firmware. You have several options for this, but Arducopter and MultiWii are the most common. I prefer arducopters, but it's more of a 'PC versus Mac' debate: there are upsides and downsides to both, and in the end, both do a pretty good job. They're basically Arduino sketches loaded on an ATMEGA, so customizing it is pretty straightforward.

I would highly recommend building it yourself, not buying a ready-made quad. It's cheaper in the long run, (search 'DJI phantom replacement parts' for instance), more fun and you'll learn more. I don't think you can write a decent stability algorithm without knowing exactly what your hardware does. One word of 'warning' though: the people behind Arducopter/MultiWii really know what they're doing. If you're expecting to write a better stability algorithm than the current ones, well, you're in for quite a challenge. Having said that, if you choose to contribute to the open source projects: power to you!

For about USD250 you can assemble a decent quad that's:
- Fun to fly
- Has replaceable parts (a necessity, you WILL crash)
- Is upgradeable (GPS for instance, or better ESC's, better motors, etc.)
- Has an open source flight controller

You should be able to make one yourself for this amount. Take for instance a nice 250 size FPV quad:
- ARF-kit: USD 100,- (Frame, motors, escs, wires, etc.)
- HKPilot (APM based) flight controller: USD 71,-
- Transmitter/Receiver: USD 54,-
- Keychain camera
- Ass. propellers (buy spares. You WILL crash!)
- Batteries (3-cell lipo) and charger

Kit:
http://www.hobbyking.com/hobbyking/store/__52863__HobbyKing_...

Flight controller:
http://www.hobbyking.com/hobbyking/store/__51498__HobbyKing_...

Transmitter/receiver:
http://www.hobbyking.com/hobbyking/store/__8992__Turnigy_9X_...

Regarding flight times: I have a slightly bigger quad (350 size). With gopro attached it weighs in about 1150 grams, and I get about 6-7 minutes of flying time with a 3-cell 2200mah lipo. I'm always experimenting on improving flight times, and I think I can squeeze a couple of minutes more out of it with a little tweaking. OTOH, 3-cell lipos are less than 15 bucks so I always bring 3 or 4 of them with me.

A couple of extra words if you're new to flying quads:
- Start off with a light, cheap microquad. For instance the Cheerson CX-10. At 20 bucks it'll cost less than a wrecked frame and 2 props, and it will teach you how to fly these things. Plus, they're light so there's no damage when you crash them.

- Please, please be careful with the larger quads. Don't fly over people, don't fly over buildings, roads, etc. Not only is this dangerous, (+2 lbs travelling at 40mph with spinning blades...) you're ruining the hobby for everybody else when things go wrong. Same goes for cameras strapped to your quad: respect privacy.

- I've said it before but here it goes again: You. Will. Crash. Don't think 'I'll be extra careful' or (in my case) 'I'm a seasoned RC pilot, I think I'm able to fly this thing without crashing': you're wrong. I promise. You will crash, and you will break stuff. Not the end of the world, but get some spare props and a frame if you can.

- I've had nothing but excellent experiences with Chinese webshops like dx.com, banggood.com or miniinthebox.com. Sure, quality is less than European brands like Graupner, but it'll work. Your first car probably wasn't a brand new Audi, but a banged up '89 civic, right? It'll get the job done just fine.

One last thing: I don't know if you have a wife/husband, but be prepared to spend a lot of time tinkering. It's an addictive hobby, I can tell you...