Suppression capacitors? What type should I use?
Those look to be bypass caps.  The value isn't that critical, but they do need to have low ESR and work to reasonable frequencies.  They should be ceramic caps.  1uF ceramic caps are plentiful and cheap.  Make sure the ones you get are rated for at least a bit more than the voltage they should be subjected to, which is too small to read on that schematic.  Getting 1uF ceramic caps up to 20V will be no problem at all.  Higher voltages are available.

Generally you don't get electronic parts at local electronic shops anymore.  There are so many different ones that a physical store can't possible stock a reasonable variety.  You get these kinds of things via mail order from electronics distributors like Mouser, Digikey, Newark/Farnell, and many others.