soft shocks, adjustable?

I'm going to ignore Phil here and suggest that if you are going to
spring for a new bike in the $500 price range that you get a hardtail
or possibly a used full suspension (the wear complicates matters).
It's not a question of snobbery on my part (my hardtail cost about
$500 in good used parts), it's just that it really is better to have a
good/great fork on a good frame than a full suspension with so-so
shocks loaded with the so-so performing goodies that have to be spec'd
on the bike in order for it to meet that price point.

I recommended a low-end dual-susp because it appears that the OP was VERY
tight on money, due both to the bike being ridden and the fact that the OP
was looking for a tweak on his crapo bike to ride on urban assaults. A
hardtail wouldn't be appropriate, and an expensive DS might be too valuable
to huck around concrete curbs and metal signposts.

--
Phil, Squid-in-Training