As a long-time 'strap wearer myself, my best advice is to just try different brands until you find the one that fits you correctly. Each brand is very different in the way their jocks fit, with some guys preferring one over the other. Myself, I prefer either Bike, Duke or McDavid. Those brands just seem to feel more comfortable on my particular body type. And there are some brands that I've tried that I absolutely hate. One example is SafeTGuard. Your mileage may vary, of course.
Buying them online is easy, and you have access to a much wider assortment of brands, styles and sizes than you would find in a local store. Of course, you do typically have to pay for shipping. But lately I find that local stores don't really carry much of a selection, which makes online buying a much better option.
There are plenty of places to buy them online. A few you might try include:
https://www.amazon.com/s/url=search-alias%3Daps&field-keywords=athletic+supporter
https://www.jockstraps.com/
http://www.internationaljock.com
http://www.jockstrapcentral.com
And don't forget eBay. I've actually bought quite a few from different sellers there.
http://www.ebay.com