Many years ago I got a screen door installed from Home Depot. They did a terrible job and I didn't realize it until it was too late to do anything about it. I'm still stuck with that door. I can't lock it from the inside unless I fight with it for at least a few minutes. Your home is an investment. There is certainly something between that high price and what you have now. You're going to have to get two more bids. How about local independant companies? They need our business. Ask your neighbors or other people you trust for referals. Get organized for this project with a thin three ring binder, labels, and loose leaf paper. Your categories will include timeline, bids, vendors (stores), ideas.

You can add a sweep to the bottom of the door to fill that gap. You can paint a vinyl door but you need to use a special primer like XIM first to get adhesion. Also you need to take the door down and remove the hardware. Without seeing the house no one will be able to suggest color updates, but I wouldn't make the door match the floor and not the walls.

The Maine screen door company might get you a screen door that fits for a bit less than $1,500. Hard to tell, but you can get a quote.

I'd add a sweep to the Lowes door and paint it.