Using a Raspberry Pi (or similar) on a non smart tv?

[haaammit]

I have a Samsung TV that will connect to my network and play some video files that are stored on my main pc but the Samsung Allshare software is dreadful and it won't play back some video files.
Would a Pi, or similar, be able to access and playback video files from my pc? Is it easy enough to do (needs to have a simple interface) and it would be a bonus if it could do Iplayer as well? I assume a wireless mouse and keyboard can connect to them? I guess they also have hdmi outputs etc?
As you can tell I'm a total noob on this subject- thanks for any pointers

 

[haaammit]

Thanks for the replies!
The TV only has the AllShare option, there's no other Smart features available unfortunately. It is an old tv. So the Pi idea will work, but a Firestick will also do what I'd like? Playback media files stored on a PC and do iPlayer? I assume it'll also do other streaming services as well?
Many thanks
EDIT: Hmm I've just been reminded we have an old ChromeCast thingy sitting about - would that work I wonder? I seem to recall it was a pita to use so it got unplugged Whatever solution, it must be controllable from the TV room, don't want to have to start playback on the PC first or anything like that, want a seperate solution if that makes sense? Smartphone control would be "OK" I guess.

 

[haaammit]

Looking at it, it appears to be a second generation one, so limited to 1080P@30fps I believe?