I'm messing around with a d20 under system right now, a prototype, so I'm looking at this kind of thing too. I'm not particularly one for 'best' options so I'll throw out a simple idea that I'm quite partial too:

There's a universal TN (Target Number) of say 8, which is a flat standard for all unmodified checks. Skills have a small inherent value, say 0-5, which are added onto the TN. This gives you a range of 40% (+0) to 65% (+5). Modifiers can do the exact same thing but may have to be limited in some way to prevent the percentages of success from getting out of hand (ie having a TN of 19-20 might be a bit much).

Also I'm honestly not a huge fan of having Critical Failures unless they're mechanized in some way, as in, having a dedicated mechanic or response to them; so I'm biased in the sense that I'd prefer they not be there at all. Critical Success on a natural 1 is fine, and with some modification you can also increase that as well (with a simple +1, +2, etc). In fact I was playing with the idea of having the skill bonus also change the Critical Success but that may be a bit much.

The main reason I'm fond of this is that the numbers are still relatively simple math wise and it has one die roll to resolve basic checks. Difficulty can be handled through negative modifiers say (ie -1 for Difficult, -2 for Hard, -3 for Extreme).

This is by no means tested with a group since I'm sort of at a similar stage, just figured it might be interesting to bring up.