What is the best skimmer for my pump size

Hi everyone
I have done a bit of reading about surface skimmers and want to buy one for our pool.
Comments have been about making sure your pump is powerful enough for the skimmer.
We have Sand Filter that came with our ultra frame pool but a skimmer was not included.
The Sand Filter is Intex Kyrstal Clear Sand Filter Pump 12" Model SF10220, it says maximum flow rate is 4,000 litres per hour ( 1050 gallons per hour).
Some people have put through wall skimmers but would our pump be powerful enough for one of those?
Or is our pool (16' x 48inch ultra frame round AGP) better suited to a Wall mounted surface skimmer and if yes is the Intex Deluxe Surface Skimmer the way to go or another type of one.
It will also depend on if we can get the product in New Zealand or not.
Also I saw someone on here saying they had a surface skimmer but it didn't work too well as their kids jumped around a lot in the pool which is what our kids will do, so will the surface skimmer still do its job?
Sorry for so many questions but two weeks ago I had never owned a pool, it's a steep learning curve!
Actually we also don't have any type of vacuum system so if we got the surface skimmer should we get one of those types that attaches a hose into the skimmer inlet or is a standalone separate vacuum the way to go?
Forgot to also ask, we have two inlets that go to the pump, so when you hook up the skimmer into one of them, what do you do about the other one? Do we just not worry about it or do you have to block it off? And how do you block it off? I can't just turn off the plunger valve as that controls the inlet that the skimmer would be coming from.