I'd recommend a piano over the keyboard and synth.

With that aside, I'd go with a digital keyboard over the synth, especially if you're a beginner. If you plan on playing an actual piano in the future, I highly suggest weighted keys, since that'll make the transition from a keyboard to a piano much easier.
ouch-sensitive keyboards are a must, and you should also make yourself use that feature. Yes, it's easier to play with that off, but it's a bad habit that'll come back and kill you when you suddenly decide to play with dynamics or when you move on to a piano. I started off playing at the same volume when I was younger, and when I decided to turn the touch-sensitive feature on in order to get dynamics in, I had to go through extra trouble. Don't make that mistake!
Try to find one with many keys. 88 is good, but if you can't get that, aim for something no less than 61 because as you continue playing, you're bound to run out of keys.
A lot of keyboards come with extra sounds and rythmn banks. If you're more into piano music, these are useless. I do know people who love messing with the different instrument sounds and built-in songs, but before you go for the expensive one that includes a zillion sounds, ask yourself if you'll really be using those.
I'm not sure which keyboard to recommend, since mine is prehistoric and is probably a discontinued model, although it works pretty well. I've had issues with older Casio models, but seeing all these recommendations for them, I guess they've improved over time.
Remember to also pick up a good pedal if you decide to get a keyboard. I recommend the sturdy pedal-like pedals over the tiny, flimsy square pedals.
You probably know this already, but make sure you do some research before getting your keyboard, or a synth if you decide to get one. Amazon usually has some nice reviews and ratings for people to check out, but also be sure to do a quick Google for reviews as well.