I've always had the most success working up "normal" reverb sounds (which I admittedly don't often have much need for ) by specifically focusing on tweaking wet/dry mix, decay time and sometimes most importantly – pre-delay times, to get things to where your clean tone sits nicely in the mix with everything else you're doing.
Presets based on the Hall, Room and Spring algos are probably where you'd want to start for this; the first 12 are usually good bare-bones starting points. If you're finding the reverb is dominating your clean signal but adjusting wet/dry mix isn't quite putting you where you want, try increasing the pre-delay to "push back" the main reverb body and tail from your original source tone…often this one setting alone can make a night/day difference in increasing clarity of the clean signal.
Conversely, if the reverb is sounding too subtle for what you need – try increasing the wet signal in your wet/dry mix while while also adjusting the pre-delay – this can "thicken" the overall reverb body/tail to make it more apparent, while using the pre-delay to keep it from getting so swamped that you start to lose all clarity.
Another thing to try with algos that have it: add a subtle (or not-so-subtle, depending on what you're aiming for) amount of modulation to the reverb. Often this can add a degree of motion, "sparkle" and perceived richness and density to your overall final tone. A little can really go a long way, so don't be afraid to experiment with the modulation rate, depth and shapes to get it right where it works best for you. And of course, setting the rate to lock onto subdivisions of your tempo (either though tap-tempo or BPM) can really add an interesting dimension to it as well to help it stand out more.
Hope this helps!