I can’t speak to the specifics of your car, but the parts you are ordering seem to be the right ones, generically speaking, for cars that use timing belts. Belt, tensioner, idler pulleys, water pump. That all looks good. I’ve always had good luck w/Gates belts. I concur w/the above advice to ask the shop to replace the front crank seal and cam seals while doing this job, provided there’s no complications specific w/this vehicle.
Since you are working on the cooling system, unless the coolant is fairly new already, I’d replace that too. So you’ll have a new pump and fresh coolant. And consider to replace the thermostat, esp if it is part of the water pump ass’y. Be sure to test the new thermostat in a pot of hot water to make sure it opens at the right temperature and the correct opening distance. I’ve had defective thermostats right out of the box, new.
If changing the accessory drive belts (serpentine, etc) is easier with the engine disassembled for the timing belt job, I’d be inclined to replace those too. If the existing belts appear to still be good, put them in the trunk, they might come in handy some day.
My own perspective. When I change the timing belt on my Corolla all I change is the timing belt and the drive belts. I test the other parts to make sure they turn/move freely, no weird noises, but unless I find a problem with something, I don’t replace anything else. My trusty Corolla is still running well on its original water pump at 200K +. I’m not saying I’m recommending this method, just saying what I do as a driveway diy’er.
About ordering parts. I don’t order parts online usually. I prefer to pay a little more and buy my parts from my local inde auto part supplier. Why? It’s not that unusual for me to have to return a part b/c they gave me the wrong version. They gave me the wrong ignition rotor for example last time I did a tune-up. B/c I purchased it locally, it was just a minor tweak to my errand schedule to take it back and get the correct one.
The other – more important, probably – risk you are taking on by buying your own parts is that if a problem occurs that damages your engine, there may be no way to prove the shop caused the problem. They’ll say the part you supplied caused the problem, and since they didn’t supply it, you’re responsible. And if you think about it, how could any shop warranty a repair they did when they didn’t supply the replacement parts? This probably won’t happen, you’ll likely get a good job for a discount, but it is a risk you are taking on.