First off things are in flux right now, the recent hiring frenzy has abated so I'm trying to geusstimate how things will play out near-term...
When things are competitive (they are headed there now, probably already there) tubine PIC is going to be mandatory or very desirable (even if their official minimums don't say that out loud). Also a few airlines seem to be getting burned after having hired very low-time, very inexperienced pilots. They might be rethinking that, we shall see.
I would probably go ahead and knock out TPIC first while you are in a position to do so, 1000 hours has been the historical threshold (although it's been much lower recently).
Only caveat there is that ASEL TPIC often doesn't hold much weight (unless it's a tactical military jet) but a Dash-8 should be fine, especially if it's in airline operations.
Frequently with prop TPIC you might also have needed some jet time, but SIC is OK for that and you already have some. I'd think even a few hundred hours of airline jet SIC would punch the ticket... they know you can be trained at jet speeds (a few prop pilots can't manage to shift to high gear).
My swag would be that 500-1000 hours prop TPIC, along with 500-1000 hours jet airline SIC, and 3000-4000 total hours would get you on the radar.
By "heavy" do you mean 737? In industry parlance 737/A320 are not heavies, but rather narrowbodies. A heavy would be 767, 787, A330, etc. Not bad to have a narrowbody type rating and experience, but I'd still say TPIC is more important. Actual heavy (widebody) international experience is certainly nice resume diversity, but the only operators who really weight that a lot have been FDX and UPS.