Do try to find some CYA (usually labeled 'stabilizer') - often sold in 4 lb. containers, which would last you several years with that size pool. Otherwise your chlorine won't last long in the sun.
Do you have a number for pH? "High" is not very informative.
As far as the pump you got, I think that sounds fine, as long as you keep on top of the pool chemistry and don't let algae get a foothold. I do not agree with the previous poster who thinks the pump is overkill. In fact, you will probably find that the filter area is smaller than you would like... But it will do the job if you are careful. Before we got our current pool, we spent a number of summers with a 1000 gallon pool, and its packaged pump/filter (rated for 600 gph) - that equipment was definitely "underkill" if there is such a word.