Do I need a double-bevel and a sliding saw?
No. Might you need one later? Maybe.
I have and would recommend the green monster:
Hitachi C12RSH Would a single bevel be fine for building your workbench? yes. You might only need the cutting capacity of a 10" non slider. Heck you might get away with a 7-1/4" one if it's just 2x4's. If you aren't sure, I would spend the extra to get a 10 or 12" slider. The Ridgid one claims the biggest capacity and from looking at the display model, it's pretty sturdy. I haven't seen one cut.
The 780 is a good saw. The 718 is also a good saw, though I would get the 780 over it. Heck even the 715 non slider is good too. Not to say that you can't go wrong with one, but nearly every miter saw I've used was a Dewalt before I got my own.
When I bought my first one, it was a 10" Skil on sale for like $80 and i tell you it was the best $80 saw ever. Stayed square, cut straight, everything you could want. Eventually I sold it because I needed (wanted) a 12" slider and selling it made room. A contractor friend has the Kobalt slider and that is surprisingly good also. Point is you don't have to go high end to get a good miter saw. No matter what you buy, the blade that comes with it will be good for cutting scrap, invest in some good blades.
Also, are you planning to get a table saw in the future? do you have one now? Maybe you should be looking at 10" saws and buy blades that will go on the table and miter both?
Keep in mind that double bevels don't have that stop at 90* so you might have to check it for square every once in a while. Not a big deal, but you're also more likely to have to check it if you carry your saw from one job to another.