The iRig is for audio connections, not MIDI connections-- and I think it's for monophonic audio at that, such as from an electric guitar or microphone, rather than for stereo audio such as a keyboard typically outputs.
If you want to connect a USB-MIDI keyboard such as the PSR-E363 to an iPad so you can use the keyboard as a MIDI controller for virtual instruments, you need the Camera Connection Kit or similar adapter. On older iPads that had a 30-pin connection port, the adapter was called the Camera Connection Kit, which contained two adapters-- one for connecting a USB cable to the iPad's 30-pin port, and the other for plugging in data cards such as are used in cameras to store photographs. But on newer iPads that have a Lightning connection port, the adapters are (as far as I know) not sold in a single kit any more, so they are no longer called a Camera Connection Kit per se, although the one you'll need does still have the word "camera" in its name-- the "Lightning to USB Camera Adapter."
As for which keyboard to get, I leave that up to you to decide. If you mainly want to use it with virtual instruments or sample players then the quality of the keyboard's onboard sounds is not so important. However, you might want to consider getting a MIDI keyboard controller that has several knobs, buttons or pads, sliders, wheels (pitch bend and modulation), and so on. The PSR-E363 will work fine as a fairly inexpensive velocity-sensitive keyboard controller, but it doesn't have any other controls (wheels, buttons, knobs, etc.) that can be used. Many of the less expensive MIDI keyboard controllers don't have much in the way of additional controls, either-- in general you will need to spend a little bit more money to get a controller that does. And if you do decide to spend a little more money on a good controller, you might even want to think about getting one with aftertouch.
