Hi Mike,
Walt's advice is pretty solid, but you might want to throw in a #2 set of hooks in case anchovies are what's in the bait tank.
There's plenty of advice on this subject, just do a search so you can see what everyone's opinion is, but you never really said what your target budget is.
1. I've caught most of my YT on a 7' Fenwick Inshore rod, with an old Calcutta 200. As Walt and Max have pointed out, your bass stuff will work, even the low-pro reels if you're just targeting calicos. I have been spooled though. This setup will be more than enough for pier fishing. It's a bit harder on an old body to fish triggersticks if the fish are the larger models (I've caught 34# YT on mine), so if you have a more traditional (non-triggerstick) rod, I feel it's easier to grind on fish with the longer butt.
2. Your 20# rig, as Walt pointed out will be very useful. You can catch up to 30# tuna without getting cornholed. But if the rod had three line ratings on it, like "15 20 30" or "10 15 20", make the 20# rating the middle or the lower rating...that way you'll have some meat left in the lower half of the rod if you hook larger fish...but remember, it's a bait rod, not a jig stick so a slightly flexible tip is nice. I like 8 foot rods, but that's just me. You can put more of a "hurt" on fish with longer rods, but they can work you also.
---If you have the budget, a Saltiga 30 is a great all around reel. If you don't have a budget then an SL 20 or 30 should be fine. Star drag reels are cheaper and everyone likes them...set your drag light...about six or seven pounds if you care about the numbers. You can always tighten it if you need it. I like Shimano because I can drive to their regional service center instead of shipping it, so I have Calcutta and a Trinidad or two. I've transitioned over to Lever drags so I like the smaller Accurates, but they're not cheap.
As Walt mentioned, you don't need a two speed...I have them but I always keep it in high speed.
If you get a hankering for a third rod, get a 30# setup...you should be able to run 40# line if you need to (that's why you bring extra line

) but you should be able to catch 40 pounders on 30# with that and you'll pretty much be set for any trip under $600.00
Sorry for so many words...