Your Arduino Uno will use 35 to 50 mA at 5V. The “joystick buttons, some rotary encoder/knobs, and a keypad” will draw a small amount of current, probably between 1 and 10 mA. Thus, power for the Uno and your controls will be well under 100 mA and can be supplied via USB without any problem. (Also see: How to get more than 100mA from a USB port.)
If your Uno enumerates and negotiates to get 500 mA via USB, you might have 450 mA available out of the +5V pin. However, in some cases if you need more than a few dozen mA to power other devices, it will make sense to get a separate 5V supply for them. (Eg, if the devices drag down the +5V and cause the Uno to reset, or if the devices are electrically noisy, like motors, RC servos, relays, solenoids.) Also, note that thread #70450 at forum.arduino.cc says you can draw 650 mA (or 3.25 W of power) when the Uno is powered via its DC power jack.
If your LED string has up to 6 or 7 WS2812B equivalents, you can power it from the Uno's 5V. Here is the all-lights-on, full-brightness calculation for six of them: 6 WS2812Bs x 3 LEDs per WS8211 x 21 mA per LED = 378 mA. For seven: 7 x 3 x 21 mA = 441 mA, which is out there on the edge.
For longer LED strings, figure on a little over 3 W of power for every 10 WS2812B equivalents. (Calculation: 5 volts x 10 WS2812Bs x 3 LEDs per WS2812B x 21 max mA per LED = 3150 mW = 3.15 W.) For example, get a 10 W (2 A x 5 V) or greater 5V power supply for a meter of 30- WS2812B-per-meter LED strip, etc. This power supply will connect directly to the LED strip's power connectors. The ground from the LED strip will connect to the Uno's ground, to establish a signal reference point.
Note, the absolute max voltage rating for a WS2812B, according to its datasheet, is 5.3 V, so use a supply whose voltage does not exceed 5.3 V. The absolute min voltage rating is 3.5 V; they will work ok on 3.7 V LIPO batteries, but 3V3 power is out of spec for a WS2812B.
As mentioned in a previous question, if your LED strip is being installed inside a desktop PC, the PC's power supply will have lots of 5 V power available, and you can hook on to one of the red +5V wires and black Gnd wires from its supply to power the LEDs, either while powering the Uno itself from USB power or while using the same +5V to power the Uno as the LEDs.