You are more advanced than I thought from the original post.
If you know you are going to need 20 different actions, you might be heading into Mega/Due territory. There are ways to do 20 different things with a single Uno, but they are more complex. An alternative is to have multiple low cost chips, each of which just controls a few actions.
I would say for now, just start with an Uno class machine. If you go with an arduino 'compatible' board, I would look towards comments about how compatible it is. If you are going to an official Arduino Uno, I would say make sure it is R3, as it doesn't need a separate FDTI programmer, it can be programmed via normal USB.
I would suggest doing something I didn't do when I bought my Uno with a vendor supplied starter kit. I just bought the first one that fit in my budget range, and just got a bag of stuff and everything was in a plastic bag, unlabelled. Instead go to the seller, and see if they have howtos for the parts you are going to buy. That way you can get going quicker, and you are also helping vendors who take a little more time to help people get started. Given you are used to El-wire, you may not need the starter bits most us of start with. There is now an official Arduino starter kit, but for my money, it is a little pricey.
The vendors that do have good howto's, etc. that I've bought from include: