Action Movie Scale
A useful thing to consider is what kind of game you want to run. What are the expectations for the action in the game? Is it brutal, slog through the mud, slip on your knees and beat someone to death with a shield? Or is it swashbuckling with running along bannisters and swinging on chandeliers?
Figure out what's a reasonable expectation of what you want to happen in play, let players know what that is, so they know what kind of stunts make sense to use.
Within that, it's also worth considering what scale the "heroes" are compared to the rest of the world. I recall old D&D has 1st level Fighters listed as "Veterans". What a veteran soldier is good at, the kinds of knowledge they have, puts them above the average warrior. So think for a bit if that's going to be the case in your game, or if they're actually just very talented rookies.
When you know what's reasonable, you can start figuring out what you want to use for a skill check. The most common method is rolling equal or under an attribute stat, usually with a D20 and modifiers. Another suggestion is to use variable dice as the difficulty - "Oh, you're doing something easy? Roll 2D8 equal or under. You're doing something really hard? How about rolling 3D10 equal or under."
Another common method some used is Saving Throws, though it can be a bit of a reach given that older Saving Throws are weirdly specific - "Uh, I guess out running this guy is like being fast enough to dodge a wand..."
Another is simply GM fiat - the player says what they're doing and you decide if it works or not. This can work real well if the players and you are both on the same page of what is an acceptable, or reasonable sort of action.
One of the OSR games, Castles and Crusades uses a simple system of two target numbers - you use the lower one if your class/race would be particularly skilled in that activity, and you add your level.
The Double Edged Sword of Non-Design
Some folks praise the lack of a system as "true freedom", but having been that kid who had to learn D&D from a box, not having real rules or examples of how to do stuff like the Old School Guide back then, mostly meant seeing lots of PCs die from the punishing mechanics. The strength is that you can basically use whatever system or set of odds you like - the drawback is you end up having to design it, and if you don't know what you want out of RPGs, it's pretty much flying blind.
I generally prefer options that demand player input and choice - their odds of success or results of action are better with clever choices, rather than relying primarily or solely on their stats. Figure out what level of action-y heroism fits for play, let the players know, and give them some leeway to take back actions until they're comfortable with it:
"I jump on the table and kick him in the face!"
"Actually, that's pretty hard, you're in armor..."
"Oh, geez. Uh, can I just topple the table over and push it on to him instead?"
"Yeah, that's an average strength check."