Just about any universal remote can do what you ask, from a $15 RCA RCRP05B or $20 URC WR7 to a $2500 RTI or Crestron and everything in between. Unfortunately, Harmony doesn't work well with Next Gen. So if you went with a Harmony, it would have to be an RF model like the 900 or 1100, which are around $250. Many RF URC models will work fine. Those run from about $70 to several hundred. You have to decide on all your requirement and budget. One of my JP1 remotes cost me $3 (it's just a cable TV remote), and it controls everything in my house using several one button macros (sometimes 2 buttons). Some people use a smartphone or iPad as a universal remote. That's a good option as well.
You'll have to experiment with the base and other blasters for the optimum placement. IR works like visible light, so imagine if you shine a flashlight from wherever you mount the base or blasters, would the light reach your devices.
I got my H900 factory refurbished for less than half that but they are becoming hard to find now unfortunately. IMHO, I think it is better than anything they offer now because I really just want a tactile remote where I don't have to look at a touch screen for EVERYTHING..
My Galaxy S4 has a built in universal remote but it isn't RF of course and all the equipment but my HDTV are operated by RF, out of sight in a cabinet without glass doors not even on the same wall as the HDTV so I don't use the Galaxy Remote app even though it does control everything quite well if the doors are open and I aim the remote properly.
I agree, refurb Harmony's are a great inexpensive option, if you can find them. I personally use the Xsight Touch for RF, but it's hard to find too. But I need to dust off my Harmony's since Logitech has made some major improvements to their software lately (myharmony only). I'll take real buttons over touch screens any day.