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.
Here is the PDB /u/gojukebox is talking about. You don't have to get this specific one, but this is what they look like. Super handy! I know there are better ones out there but I can't seem to find any at the moment. They have spots for OSD which is nice.
Here are a couple other things I would grab:
Lipo voltage checker: Lipo Voltage Checker/Warning Buzzer
Lipo battery bag: Bluecell Silver Large Size Lipo Battery Guard Sleeve/Bag for Charge & Storage
Get more props. A lot more. Go to the Bulk prop guy while he still has some in stock and buy from there. Cheapest deals on the internet.
Here is a list I threw together for you. I threw in a couple extra options so if you have questions about choosing between 2, let me know. That kit you linked isn't bad, but you for sure want to at least update the flight controller and get a naze32 or clone of it instead of the CC3D it comes with. Just giving you some options.
Don't get that transmitter you linked. You want to get one of the 2 I linked, perferably the Taranis. Buy nice or buy twice. Cry once and buy once. You don't need the top of line stuff, but you want a Transmitter that will keep up with you.
FPV Goggles: Quanum DIY FPV Goggle V2 w/5 inch LCD Monitor (Kit)
Video Rx: RipaFire® TS832 FPV 5.8GHz 32 Channels
Video Tx and Camera: Eachine 700TVL 1/3 Cmos FPV 110 Degree Camera w/32CH NTSC Transmission
Transmitter: FrSky Taranis
Transmitter: Turnigy 9x
Flight Controller: DragonFly32 PRO
Flight Controller: Naze32 Acro
Motors: Sunnysky X2204s KV: 2300 Motor
ESC: DYS BL20A BLHeli Mini ESC
Frame Kit: ZMR 250 All Carbon Mini FPV Frame
Charger: IMAX B6AC V2 Professional Balance Charger/Discharger
Props: Gemfan 5030 (You will want to buy at least 10 sets of these)
Battery: Turnigy nano-tech 1800mah 3S 25~50C Lipo Pack
Power distribution board: PDB / Power Distribution Board Special for 250 QAV250 H250 Mini Quadcopter
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 and velco!
Only other thing will be batteries, leaning towards 1800mah or 2200mah.
I would start with like 3 2200mah batteries. They are bigger and heavier, but will give you longer flight times. You will want that longer time in the air once you first start. After you get comfortable, you can go down to the 1800mah or 1500mah to get less weight and go faster and do more tricks.
And Will this be able to occasionally carry a GoPro without issue?
It will easily carry a go pro, but be sure you have a case because you are going to crash a lot when you first start!
If you have any questions about anything, let me know. I am happy to help!
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!
Here is a starting parts list I made for you for a 250 that should keep you right around $300. Let me know if you have any questions!
Transmitter: Turnigy 9x
Flight Controller: DragonFly32 PRO
Motors: Sunnysky X2204s KV: 2300 Motor
ESC: Eagle 12a blheli one shot ready
Frame Kit: ZMR 250 All Carbon Mini FPV Frame
Props: 10 SETS - BLACK/BLACK GEMFAN 5030 2-BLADE MULTIROTOR
Charing XT60 cable: Charge Cable w/ Male XT60 <-> 4mm Banana plug (this does not come with the charger)
Battery: Turnigy nano-tech 1800mah 3S 25~50C Lipo Pack
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 and velco!
Alternate FC: Naze32 acro
Alternate motors:Emax MT-1806 2280KV Motor