1)  Will a 5A 250V fuse work as the fuse?  I'll have a monitor which is 1.5A, a Pi which is .3A and an LED light strip for the marquee.  If not, what Amp fuse should I use?
To answer that, we'll need to know some details about your LED light strip.
- Specs? Link? Type of LEDs? (single color or RGB) Number of LEDs in your marquee?
With a 5A fuse, you've got about 3A to play with which would allow 150 single color LEDs @20mA each or 50 RGB LEDs @60 mA each. (20mA per channel)
2)  I bought some fully insulated .187 female spade connectors for 14-16 AWG,  the power strip has 14 AWG stranded in it that I plan on wiring to the switch.  Are these cool to use?
Yes.
As always when dealing with mains power, make sure that you have both a solid mechanical connection (twist test) 
and a good electrical connection. (<2 ohms) 
Scott