That will work fine. The reflector is decent, but not the best. I didn't see if it listed the brand ballast or if it's magnetic or electronic. I don't know where you heard a ballast can make a bulb 27% brighter. Some bulbs run better on electronic ballasts while some work better on electronic, but 27% is a little far fetched. You can check
Sanjay's Lighting site and compare bulb/ballast combinations. I also didn't see if it mentioned the brand bulb. That is extremely important. You can have 1 250w MH bulb put out 35 PPFD while another can put out 120 PPFD on the same ballast.
There is no real difference between a DE (double ended) bulb or a SE (single ended) bulb except you need a reflector with a UV shield with a DE bulb while a SE bulb has the UV shield built in. They are very similar in price. You can buy good name brand bulbs or cheap Ebay bulbs in SE and DE. You will pretty much get what you pay for. FWIW, I buy the best 175w bulbs available and they cost me $70 each.
If your tank is 4", you need 2 bulbs/setups.