I've never seen a good all-in-one kit, but the various bits are cheap. Here are some amazon links, not sure if they work everywhere, but you should get an idea. If you're in the UK, I'd recommend a supplier like Bitsbox, because they have a relatively limited range, so it's less overwhelming.
1. These Pots look OK
- you should be able to force them into the pins on the breadboard, and they're cheap.
- You're looking for 10-50k Linear pots, also often called B pots. So B10k is good, A10k isn't good. Single gang = one track. Dual gang = two tracks (like for a stereo volume control) you don't want dual gang for this kind of prototyping.
- You want pots with PCB pins you can force into the breadboard. Some pots have solder lugs - to use those, you'll have to solder on some bits of solid core 22awg wire, which you can then force into the breadboard. Remember, if you buy the wrong kind, it's probably quicker to buy some more, rather than messing about trying to get them to work...
- The neatest pots for breadboard are Alpha Vertical pots like these: http://www.bitsbox.co.uk/index.php?main_page=product_info&cPath=94_325&products_id=2287 with the tabs snipped off.
2. This Breadboard looks perfect
- Any common breadboard will work.
3. These Jumper wires are messy but quick and easy
- Or you can use any SOLID CORE reasonably thin wire, 22AWG is good, and you'll need wire strippers
4. I use these really tiny tactile buttons
- Any through hole tactile buttons should work - 2 pins or 4 pins, experiment to make sure you've found the pins that are switched!
- They're quite small and fiddly, but come in a bag of 50 so you've got plenty of spares...
5. I'd buy this bundle of LEDs
- Any LEDs will work. You'll probably need wire trimmers to make them a bit shorter and neater in the breadboard. When trimming, cut the long lead longer than the short lead, so you know which way round they go.
- Some LED bundles include flashing or multi-colour LEDs, which could be really confusing in this context.
- RGB (red, green, blue) LEDs are also fun if you connect them to 3 x PWM outputs.
6. If you use LEDs, you'll need resistors to protect the LEDs from excess current
- Any value from 220 ohms to 3,000 ohms (3K) should be fine - smaller the resistor value, the brighter the LED (ie 220R is very bright, 3K less bright). If you have 'ultrabright' LEDs, then they'll be REALLY bright with 220 ohm resistors, you might want 5k or 10k. They'll work fine, just burn your eyes 
- The resistor type (carbon, metal film etc) doesn't matter here. But be careful with the value. If you buy 220K rather than 220R or 220Ω (same thing) then you won't be able to see your LED glowing, it will be so pale.
- Resistor value clarifier: Ohm = Ω = R. 1000 ohm = 1K. So 1000 Ohm = 1000Ω = 1000R = 1K. You sometimes see the notation where people write 4.7K as 4K7, I think because in old printing systems, the . might have got lost.
HAVE FUN, remember you probably can't break anything much.
You can now make this: https://www.instagram.com/p/_roKoUjmYD/
