This is a sticky area, and a quick search says it has been discussed here a lot.
I am leery of posting anything without some cautions. You may know some or all of this, but I have know way of knowing that and don't want a chart I made to lead anyone down the garden path.
The first milliseconds of a model rocket engine are very dynamic, and exact analysis is sticky. The community uses a number of rules of thumb to simplify things. The 5:1/3:1 rule is basic. Go below 5:1 at your own peril, remember the rocket does not move until the thrust equals its weight - acceleration at 3:1 is HALF 5:1, not almost two thirds.
If I understand the definitive rules, they set an absolute requirement of a 3:1 ratio of weight on the pad to the certification average thrust. This is the law, but may or may not be enough, depending on the thrust curve. It may be marginal for motors that build thrust slowly (and more than enough for those designed with a high initial thrust spike that lasts long enough to get the bird off the rail). A 5:1 ratio to certified average thrust is probably a good place to start (until you have a reliable, detailed simulation).
Don't bet your life on maximum or initial thrust without supporting analysis. Maximum thrust is published for most motors. ThrustCurve speaks of "Initial Thrust", arbitrarily defined as the average over the first half second. In real life, what matters is the thrust curve (and integrated acceleration) from first motion to the top guide/button/lug reaching the top of the rail. At constant 4g acceleration (5:1 ratio) that ranges from 0.15 seconds to 0.4 seconds from first motion. Also bear in mind where your guides are - you get no credit for rail below the top guide. If your guides drag or catch on the rail, all bets are off.
The rule of thumb goal is 50 feet/second, or greater than four times the wind speed. This is the where the physics actually meets the road and the rocket should be aerodynamically stable, but you can only know you meet it through detailed calculation. And at constant 4g acceleration, that takes about ten feet of travel . . . . If you meet all the rules of thumb and charts but your rocket is in fact at only 25fps as it leaves the rail, it may or may not fly straight, and you will not have the opportunity to debate the issue with Mother Nature.
Bottom line is, use the charts, and rules of thumb, with discretion. Even the engines approved by the kit manufacturer are not not necessarily safe if you built, finished, or equipped you rocket in a way outside the assumptions built in to the recommendations. If you are anything less than 6-8:1 and your rocket has anything to it tougher than paper and balsa or substantial mass, you would be well to run a verified and validated simulation for your rocket and motor, ensuring the curve in the sim file matches the actual curve from the manufacturer (or cert authority) for your motor.
That said, here are two charts for smaller rockets (that absolutely do not supersede any published RSO chart, from any agency – and, if I slipped a cog on them, please let me know so I can take them down). OK to use these for a rough ballpark idea of motor choices NOT for the definitive safety check of any rocket.
