Welcome to Warwickshire.
For TV, don't forget all TV's are sold with Freeview built in. Lots of channels (including news channels), and as it says on the tin, it's free; just hook up the antenna. Special movie, sports, and US orientated channels will need cable or satellite.
Trash pick-up in Leamington is weekly; week 1 for standard waste, and week two for re-cycling (grass and garden cuttings, food waste, tin cans, paper, cardboard, glass, etc.). As already said, it's included in the council tax.
There are no really bad areas in Leamington, just less desirable areas, better areas, and much better areas. Don't rule out Warwick or Kenilworth either. Kenilworth is smaller, but has a shopping precinct with many stores and banks.