I'm a string bass repairman in Reno, Nevada. I see lots of different types of basses, and as many different types of players and applications. Many of my clients are Jazz musicians, some play Bluegrass, and a number of Rockabilly guys, too. From my experience with Kay and Engelhardt basses, on a budget- try a K&K Bass Max. It is easy to install, and under, or about a hundred bucks last I checked. They sound great for a number of applications on these basses. They make a more expensive Rockabilly model, which is not really necessary, in my opinion.
If you are going to play loud, with a large amp- you may need a magnetic pickup, like The Pierre Joseph's String Charger, or Krivo...or a Schaller- which have been around a long time. YOU WILL have feedback issues, playing too loud with any pickup... standing off-axis of the cabinet is critical.
If you are going to play mainly Jazz, I recommend a Gage Realist for low volume small combo gigs- or a Fishman Full Circle, with 1/4-20 threads, if you already have an adjustable bridge on your bass. If you still have the original Engelhardt bridge on your bass, firstly- I'd be very surprised. They are the worst part of those basses, a cheap, flatsawn maple warp magnet. You should have a high quality maple quartersawn adjustable bridge installed on your bass, if you don't already have one.. It makes a big difference in a number of areas. There are a lot of pickups on the market..some show up on Ebay, after players try them and find that they are the wrong pickup for their application. Hope this is of some help- Good Luck!
P.S. I have a Full Circle on my Herman Lowendall carved bass.
I have used a homemade magnetic pickup, The Realist, Underwood, Polytone, DeArmond, Fishman BP-100, and now the Full Circle.