for starters lets go back to what giles villenueve suggested to make it a drivers formula but with modern provisions
1 unlimited engines, but nowadays add in a max fuel quota to limit the power that way (but ensure there is at least as much power as today), if you can build a more efficient engine you get the benefit rather than currently where either you're pegged back or the less powerfull engine is allowed ot be developed, then make it so every engine maunfacturer has to be prepared to supply every team with the same engine for a fixed limited price. they probably won't have to but it will deter use of unobtanium (BTW nice use of the phrase in avatar mr cameron), engine ecu's to have no driver controlled maps, cars to be run on rolling road after race to ensure power curve is the same in each gear to rpevent traction control by another means. no refueling so if you can make the power on less fuel you benefit from reduced weight.
2 limited tyre size, no more than 15 inches at the rear, this along with 1 should ensure that throttle control is at a premium. 1 stock tyre compound (excluding wets / inters ) for whole year ok so it would be too hard at some circuits and too soft at others but guess what? it's tough learn to drive around problems like they used to, anyone remember hunt in 77 gambling and almost succeeding by doing a race on qualifiers and coping with the overheated tyres later on. if you cant work out how to look after tyres or work with tyres that don't grip then you're not the best in the world. 4 sets of tyres allowed for a race.
3 rear downforce to be reduced to 1976 levels. so thats simple single plane wings and a flat bottom from where it currently starts to the furtherst rear point so no diffusers, plank to be doubled in height to limit low running. front wings to be as wide as today but to be mounted higher so as to take them out of ground effect, once again a 76 average height would be a good place to start. the bottom of the body work at the point where front wings are mounted is to be lowest part of car (excluding the plank) if any part of the body work is higher than it then that becomes the lowest point reference for anything further to the rear, this eliminates the current high noses and once again simplifies underbody aero.
4 manual H shift transmissions and clutch, i can cope with it so the best drivers in the world should be able to, no antistall clutch as it won;t be needed with the following point
all engines must be able at the end of the race, whilst at working temperature, to be started by an onboard starter motor, they used to be required to have one but it was dropped sometime after 77 as teams were fitting such small batteries and engines were so temperamental they didn't work but with today's engine management this won't be a problem, if it is then rethink your engine.
engine driven alternators to be banned, all electrical power from batteries (or other electrical storage techniques) which cannot be changed durring a race but it's up to you if you wish to have big enough batteries for a race or recharge these from an energy recovery system and if you wish to use the electrical energy to provide extra power you can (and no limit on how much or how long) but just make sure there's enough left to start that engine at the end, cars minimum weight to be measured without batteries / kers fitted to encourage development of lighter solutions. all storage systems to pass an extensive impact / fire / short test to prevent giant "bomb" capactitors being used and once again encourage safe solutions for road use . you can charge durring a pit stop so we may see the development of quick recharging electrical systems for road use.
mirrors / mountings to be a spec design, make them a senible size so they at least let you see the rear tyres and the mounts will make sure they're mounted in the traditional position not on disguised turning vanes.
apart from the front and rear wings, body work to form a smooth surface with no protrussions larger than the camera pods i.e no winglets, vanes, barge boards etc it there is any doubt about a part it must be agreed to by every other team. no part of brake cooling assemblies etc allowed to the outside of the wheel's spokes so no spinners etc, wheels to have be increased from 13" to 18" diameter, lets get the suspension doing the work rather that using tall tyre walls as suspension, also it is stupid to have wheels smaller than just about new car available today. wheels to have to allow a certain amount of light to pass through the area between the rim and the hub flange, this will mean spectators can see the brakes glow and prevent complicated areo fins as spokes.
brake materials etc to be as current regs, tyre size/ aero grip will limit how braking anyway.
suspension to be to current regulations with track width/ wheel base / car length / width going back to 1976 dimensions, this was when the maximum limits were first imposed and set by the simple expedient of taking the largest cars in each area as the maximum.
fuel type to be free with the provision that it must be provided by a commercial motor fuel supplier and be available at 20% of that companies forecourt pumps. sample fuel to be compared to fuel obtained from a random forecourt belonging to that company. if the fuel's legality is in doubt then it fails, no appeal.
hopefully we'd end up with a series where the driver matters and technology didn't take the skill out of driving but at the same time encourage the development of engine efficiency and better fuels / energy storage and inovative designers.