One thing I suggest avoiding: you often see a 113H sold as a combo with a Penn Slammer rod. The Slammer rod is very low end...essentially a give away. On sale the combo price is often $100 or so: $129 is a common price. You are buying a 113H (a very solid reel that sells in that price range) and a rod that may last a half dozen trips before the eyes start to pop. You will also see the Penn 330GT2 bundled with the Slammer as well for the same price...heck sometimes you see it for less WITH the slammer than without it!
You could of course buy the 113H/Slammer combo, and then go buy a decent rod. $60 to $80 can buy a lot of good boat rods. Penn Stand Up Mariners are very solid rods in that range; many others as well.
I don't know if you want to consider a leverwind reel or not. Two to consider are a Penn 330GT2 (or previous model GTi), which is about $100, a Penn 330 LD (lever drag and level wind) for about $140, or an Okuma Titus T20L (a level wind, lever drag), which is about $120 on sale this year. I've never use one, but I expect the Titus T20 (the non-level wind model brother of the T20L) would be a solid reel as well.
All of these I've mentioned are fine for heavy spring and fall trolling in the Bay. Summer trolling you can go a little smaller easily (Penn 320s, Titus 15L, etc).