Incoming wall of text.
cover all of your prerequisites. Ryu is a little on the average speed side, but he's not too bad.
covers all of them better than the ones above except for the BnB FAir (that's BAir or UAir or NAir for him) and the "short ranged" comment. (though only some moves suffer from this)
covers them all except for "good grab". It's her biggest flaw, but she can kill super early (same as MK) with UAir -> UpB strings. (Watch Leo vs. Mr R and Nairo vs. Dabuz at Paragon for examples of both.)
is in the same boat as ZSS. everything else is spot on but his grab is trash.
is a great choice too obviously since everything you don't care about is stuff he doesn't have. His grab is pretty poor but everything checks out (even the comment about the FAir, his FAir actually sets up his ground moves amazingly and can gimp)
would be perfect for you, but he's just a bit too slow so I didn't put him in the list of those who have everything you want. His punishing isn't slow in the slightest, however.
I recommend you consider those five too.
4th fastest running speed, has his blaster and decent melee range, good fast jab and all his tilts have a lot of good uses, his dash attack sets up for combos and his grab is nice and fast, good for punishing shields. He doesn't have very reliable grab followups, but they do exist. His FAir is good and can set up for stuff back on the ground, though his other aerials are better, and for killing early...USmash, UAir. That's all.
yikes this guy's scary. Decent ground speed, good range, amazing jab and tilts, good dash attack and grab, amazing FAir, and kills at like 60 with true Shoryuken which can be combo'd into.
I can't say anything about her that hasn't been said a million times. Let's just say she covers all your criteria and then some, and move on.
is just awesome. His jab is a bit iffy but it has quite a few uses so I gave it a pass, and everything else checks out amazingly.
Watch ZeRo or MVD and you'll get the gist of what this chimp can do (and he can do a lot.)
There's ten options for you that completely/mostly fit your criteria. Hope this was helpful!