I help out with a project [1] that teaches middle-school-age children how to build and fly multicopters with an annual competition in Atlanta. A lot of people wonder if "drones from scratch" projects is the right level for middle school kids, but it's similar to PC building: Although they seem difficult to someone who has never done it before, all the parts are built for you. You just have to put them together.

If you think it'll help you decide on beginner-friendly parts, here's the kit we use. This is in no way intended for racing, but this will put someone in the air that wants to get into the hobby.

For a flight controller, we use KK.2s [2] and CC3Ds [3]. The KK.2 board is programmed through a built-in screen, so it's useful if you want to make changes on the fly (no pun intended). The CC3D is tuned by plugging it into a computer running LibrePilot [4][5]. The advantage to that is that LibrePilot gives you much more features/customization options than the KK.2's tiny screen does. I've also found the CC3D to be a little more reliable.

Our transmitter/receiver combo is the FS-i6 w/ the FS-iA6B [6]. Nothing special, should give you about a half-kilometer of range. If you're willing to spend a bit more, I highly recommend the Turnigy Evolution [7]. It has much nicer gimbals, and feels a lot more comfortable in the hand. The only disadvantage you'd have with this one is that switches/knobs are limited, so if you want to make cool peripherals you'll have less options (fun fact- if you hook up directly to a channel output on a receiver, and bind that channel to a switch on a transmitter, the servo will move in either direction! Lots of cool things you can do with that)

For motors/ESCs, this MultiStar motor/Afro ESC combo pack [8] is pretty nice. The motors can break if crash hard, but the hardware you get for the price is excellent. If you get them, heads up: the axle that rotates with the motor sticks out to be lower than the base of the motor, so when you mount it, make sure that it won't drag on anything when it spins. Most frames have a hole for this purpose, but I've had issues with this in the past.

When you're not racing, propellers aren't something you can go wrong with (well, at least compared to other parts). With your price range and the assumption that you're just building a simple multicopter for flying in a field somewhere, 6-inch props (Example [9]) are really all you need.

Batteries are something that really depend on what kind of flying you're doing. You can go from tiny 1-cells for brushed micro quads [10] to high-discharge 4-cells for racing [11], all the way to massive 30,000 mAh LiPos for, I don't know, agriculture or something? [12] I'll have to make guesses about what kind of drone you want to build, but unless you're doing something extreme, a simple 3-cell 1500 mAh LiPo should work fine [13].

As for a frame, I recommend you 3D print one if you're not racing or trying to do acro flying. There are a million on Thingiverse, but there's one called the Crossfire that I really like [14].

Again, I have no idea what kind of multicopter you're trying to build, and there are so many ways that the parts list would change if you were trying to get into racing or full autonomy or something else. Other than the frame, this is what we start kids off with, and it's proven to be an effective way to get people into the hobby.

[1] https://www.g3robotics.com/dfg
[2] https://hobbyking.com/en_us/hobbyking-kk2-1-5-multi-rotor-lc...
[3] http://www.getfpv.com/openpilot-cc3d-flight-controller-strai...
[4] https://www.librepilot.org
[5] https://github.com/librepilot
[6] https://www.getfpv.com/flysky-fs-i6-afhds-6ch-transmitter-an...
[7] https://hobbyking.com/en_us/fpv-racer-radio-mode-2-white.htm...
[8] https://hobbyking.com/en_us/multistar-afro-combo-pack-2206-b...
[9] https://hobbyking.com/en_us/gemfan-propeller-6x4-5-black-cw-...
[10] https://www.getfpv.com/tattu-220mah-3-7v-45c-1s1p-lipo-batte...
[11] https://www.getfpv.com/lumenier-1300mah-4s-60c-lipo-battery-...
[12] https://www.genstattu.com/tattu-30000mah-22-2v-25c-6s1p-lipo...
[13] https://hobbyking.com/en_us/zippy-compact-1500mah-3s-25c-lip...

Side note, this is my first post to HN. I have no idea what I'm doing, and if I'm breaking any unwritten rules or something please tell me! Thanks