Welcome to the forum!
I take it that you're looking for a powered sub. Will you be connecting it to the receiver or to the computer directly (more of a question about connections and not the sub itself)?
I haven't priced subs in a while, but I recalled Dayton subs at Parts Express being a popular recommendation on this site back in the ~2009 timeframe for that price range, so I checked out their site. While not a Dayton, they have the
BIC F-12 priced at $200 with free shipping, and it has three reviews from very happy customers. Amazon has that same sub, with 82 reviews (most of which are 4 and 5 stars),
for $187 (I don't know if regular shipping is free because I'm a Prime member). One issue might be the size of it in your room.
That was just a really quick search on my part. You might be able to find that sub for less elsewhere, or people here might give you even better recommendations than that sub.
I don't have have any opinion on front versus down firing. I've used both with good success.