For most saltwater fishing involving casting, I prefer a spinning reel. You can throw light baits and shrimp with just a circle hook or a jig head easily with a spin cast that you just can't do as well with a baitcaster.
Hanging rods of the sides while drifting, a baitcast round reel is fine. When it comes to jigging back and forth off the bottom, I prefer a round reel or low profile baitcaster.
For what you are wanting to do, I would recommend a 7' Med-Heavy to Heavy rod (I prefer Med-Heavy) and a Spinning reel. $150 is a pretty tight budget for a rod and reel. Take a look at the Penn Fierce II4000 $70 and for a rod look at Shakespeare Ugly Stick 1 piece rod $80.
Remember you get what you pay for. The reel's performance is important and at this price point, many rods are all going to perform about the same.
Capt. Craig Copeland
2013 Nautic Star 2110 Shallow Bay Boat
Nautic Star Boats Pro Staff (nauticstarboats.com)
Redneck Fish'n Jigs Pro Staff (redneckfishn.com)