That question could be the start of a spirited discussion for sure. I'm not a beach hunter, so I can't help on that part of the question. But I've used a bunch of detectors over the years inland, including some time hunting the low country of South Carolina.
For me, if I could only have one detector, it would be the Fisher F 75 LTD. It can be set up to hunt almost any condition from very trashy to pure woods camps, and has very fast target separation and depth. And I have used it in the Low Country, so I know it will work in the sandy coastal soils. But price is well above your desired range.
So, if you are hunting primarily the low country, and in your price range, I'd get either the best Fisher F series with a DD coil that you are willing to pay for, or if you will be hunting mostly heavy iron sites like old housesites, I'd consider the Fisher Gold Bug Pro. Not the depth of the F75, but great discrimination and a nice coin hunting detector as well.
The Tesoros mentioned are very good detectors as well. I've used both the Tejon and Cibola and in fact still own a Tejon for folks to use that I take relic or coin hunting who don't own a detector. Either are easy to learn quality detectors.
I don't have the personal experience with the Whites.
Whatever you get, take time to learn it and you'll make some great finds! And use a quality set of headphones. For me, there's no better hobby than metal detecting. But Dave gave good advice. If you are starting out, borrow a detector and make sure mteal detecting or relic hunting is for you.