I'd recommend using the Guild Dice system for the players, so they can share their dice rolls. Each Player can have a Campaign with your Roleplay Name or Character Name to make it easy to look up too. Personally I have always had players have a hider at the bottom of their IC posts with their result as well. Alternatively, if you don't mind players rolling offsite,
random.org or google diceroller can be quicker.
Roll to Dodge would be a good system, but heads up it is very swingy. But I think not having an action every turn would counteract that quite well. You could have each character be specialised in an action and get a +1, so maybe they don't end up in hospital and they have a small chance of a 7/Super good result, which is only possible if the character has that class/training/experience/ect.
I ran a glorified Boardgame on the forum a few years ago
here. For Combat you had to roll above a certain number on one dice, so 3+ was amazing, 4+ was pretty good, 5+ was bad and 6 was terrible.
Then for skill checks it used a pool dice system - Agility 4 meant the character rolled 4 dice for an agility test and Luck 2 meant a character rolled 2 dice for a Luck check, for example. Every 6 was a success, or 5+ on easier tasks. It meant that characters had good flavour because they had some things there were really good at and other areas other characters exceeded at. Also, sometimes players would be rewarded for multiple successes sometimes like getting extra loot, which I think they enjoyed.