You should definitely start with something like a hubson or Syma. I started with a Syma x5c and it was great. I flew with it for about a month, learned the basics, and knew I wanted to move onto bigger and better things.
If you are wanting to build your own, I would suggest learning how to solder. It's not too hard to learn and you you will be able to do repairs and upgrades. You will really want to know how to repair your quad because I promise you will break something :). I put a parts list together for you. But again, I would suggest starting with one of the quads listed above. You will want to crash with that instead of your built quad. But if you just want to jump into it, I won't stop you. Let me know if you have any questions!
FPV Gear: Quanum DIY FPV goggles or FatShark Predator V2
Transmitter: Turnigy 9x
Flight Controller: DragonFly32 PRO (there are many choices out there for FCs, this is just the one I used, and I know the naze is solid)
Motors: Sunnysky X2204s KV: 2300 Motor
ESC: FreeBirdRC.com "Eagle" 12A SimonK RapidESC Speed Controller
Frame Kit: ZMR 250 All Carbon Mini FPV Frame
Props: 5030 Airplane 2-blade Propeller Props 50x3 CW Multi-Copter Quad-Rotor 2-Pairs
Battery Charger: ORIGINAL SkyRC iMax B6 Super Multi Charger Balancer for Lithium (Li-po,), Ni-cd, Ni-mh, and Pb Battery
AC Adapter for charger: Adapter Supply Imax B6 Lipo Battery Balance Charger Us Plug+power Cord/power Cable
Charing XT60 cable: Charge Cable w/ Male XT60 <-> 4mm Banana plug
Power distribution board: Hobbyking Multi-Rotor Power Distribution Board
Battery connecter: XT60 Male w/ 12AWG Silicon Wire 10cm (5pcs/bag)
Lipo voltage checker: Lipo Voltage Checker/Warning Buzzer
Lipo battery bag: Bluecell Silver Large Size Lipo Battery Guard Sleeve/Bag for Charge & Storage
You will also need zip ties, velcro, and heatshrink. You will also want to make sure you have extra wiring for WHEN you mess up your solders.
So this is pretty much my build and its solid. It might be a little over $200, so I can help you bring the price down if that is an issue. These are low to midgrade parts and are all pretty sturdy.
Just remember that going from a hubsan to a 250 is a big step up. These are so much more power, but its totally worth it! Let me know if you have any questions
Transmitter: Turnigy 9x
Flight Controller: DragonFly32 PRO
Motors: Sunnysky X2204s KV: 2300 Motor
ESC: FreeBirdRC.com "Eagle" 12A SimonK RapidESC Speed Controller
Frame Kit: ZMR 250 All Carbon Mini FPV Frame
Props: 5030 Airplane 2-blade Propeller Props 50x3 CW Multi-Copter Quad-Rotor 2-Pairs and I have been using 5045s, I think I will stick with them. Giving me a lot more punch.
Battery Charger: ORIGINAL SkyRC iMax B6 Super Multi Charger Balancer for Lithium (Li-po,), Ni-cd, Ni-mh, and Pb Battery
AC Adapter for charger: Adapter Supply Imax B6 Lipo Battery Balance Charger Us Plug+power Cord/power Cable (this does not come with the charger)
Charing XT60 cable: Charge Cable w/ Male XT60 <-> 4mm Banana plug (this does not come with the charger)
Battery: FLOUREON® 2 New 3S Lipo Battery 11.1V 2200mAh 25C RC Rechargeable Battery Pack with XT60 Plug. I also use the 1800mAh note that I am trying to be a little more agile. Also, the have a variable C instead of a static like the 2200mAh I listed. Thats up to you. The bigger one gives longer flight times and less agility but you might want that at first.
Power distribution board: Hobbyking Multi-Rotor Power Distribution Board
Battery connecter: XT60 Male w/ 12AWG Silicon Wire 10cm (5pcs/bag)
Discovery Buzzer Discovery Buzzer
Lipo voltage checker: Lipo Voltage Checker/Warning Buzzer
Lipo battery bag: Bluecell Silver Large Size Lipo Battery Guard Sleeve/Bag for Charge & Storage
You will also need zip ties, velco, and heatshrink!