Searching for an emulator console

I’m looking for a console the family can have fun with (myself, my wife, 8 year son 6 year old daughter). I would like the system to be able to play old arcade roms and from the older game consoles. I know about Mame, and other emulators, but not much more than that. Things that are important:

Play Lego Dimensions. This is HUGE for my son. This was made for the PlayStation 4, PlayStation 3, Wii U, Xbox One, and Xbox 360. There's a gameboard needed to play that plugs into the game system, so I think (not positive - still trying to understand how all of this works) the console I buy needs to be one of these (PS4, PS3, Wii U, Xbox One, and Xbox 360). Have of any of these been modded to be able to run emulators?

Play android games

Install Amazon Marketplace to be able to install/play some Amazon exclusive android games

Wireless controllers - Up to 4 if possible

Not important, but would be nice:

Able to install home theater software and movie files (would I use the controllers or tv remote to navigate?)

Use as a dvr

Maybe a wireless keyboard (although not sure what I would need this for)?

This would be hooked up to a Roku TV - if that matters.

I’ve seen people use Xbox and I think also Wii consoles to make Mame emulators. Is one system better than the other to use as an emulator, or the other things I would like to do. What about Playstation? Is that an option?

Thank you.

**Edit: after some research, it appears that the system I choose to run emulators on needs to be one of the consoles that Lego Dimensions was made for. The reason is that the gameboard (portal base) plugs into specific machines. After searching on Amazon it appears that the gameboard/portal base used in Lego Dimensions can be shared between Wii, Wii U, PS3, PS4, however both Xbox One and Xbox 360 seem to need their own gameboard/portal base. Would a gameboard for Xbox One also work on Xbox One S?

So, I guess the real question is which game system that Lego Dimensions was made for (PS4, PS3, Wii U, Xbox One, and Xbox 360) would be the best choice to run emulators, and, hopefully as a bonus, can also do some or all of the other things on my wish list above.

Thanks to everyone helping. Much appreciated.

Best match for all you want is the shield. It will run RetroArch for older games, it is a console, so it will play PC title games, and it is an Android so it will play app games. I run my with a Bliss-Box adapter so I can use retro controllers but it comes with its own wireless controller. There is not much fooling around to make it all work, so I think its your best bet. You could go with Current gen consoles and hack them up so they play retro games but they will not work for all you asked for (aside form maybe the switch). The Switch would be the runner up IMO, I use that with Retro Arch also but since mine is hacked I can get anything on it. I'd say the switch is more fun but more work. I think the shield may not run Lego Dimensions but not sure, I see the Switch does.