Looking for a good small subwoofer...

I wouldn’t use the crossover in a budget sub unless sound quality not important.

I’d run the sub full-range using either a line-in (RCA) or speaker wire coming off the main amp’s speaker connection posts. Use the sub’s volume control to blend things and the frequency knob to eliminate higher-frequencies.

You can get away with a single sub in a small room.

Personally, I’d always go with a 12" sub over an 8 or 10 inch.

RELs in my system 

Am presently quite satisfied with a pair of REL Strata III’s, 100 watts each, 10 inch driver, rated to 18Hz (though when I tested them I got a response at 16Hz), made in the 1990’s.

They’re accurate with no muddy, sloppy boom.

It took a little while to find two good deals, but I eventually rounded up two for less than half the price of one new.

I also have the mk10 speedwoofer . Paired with elac 2.0 unifed ub52 speakers  love the sound. 

Had a dynamo 800x from Martin Logan.  Did the job, sounded good and wasn’t huge.