The extra strainer basket will help catch extra stuff, but the pump strainer basket will also catch junk, if you don't have the room you will be fine with the one. I am putting an in line basket before my pump basket to help out with catching junk, but it would be ok without.
Your bottom drain would not be piped through your skimmer, you should have two lines one to your skimmer one to the drain, then to the pump. Have the two lines join before the pump. I put in ball valves to regulate the flow between the skimmer and the drain.