Ah, typical street car mentality. Big is cool, big is better, big is fast. Nope not always true. Now they do look cool, but it won't necessarily make your car faster.
The problem with wheels and tires is they are heavy. And bigger tires and wheels are heavier. But you get more grip, right? Dilemma. You will get more grip with a wider bigger tire, but only up to a point. Its one of those diminishing return thingies. Yes a 205/50/15 is better than a 165/70/14, but there are other things to consider. A rule of thumb is that every 1 lbs of wheel/tire weight is = to 3-4 lbs of car body weight. Did you spend a whole bunch of time stripping out the interior to make your car lighter and faster??? So an extra 3 lbs per wheel = 36-48 lbs of car weight.
More on being heavy: Inertia. This is the energy in the rotating mass (weight) of the wheel plus tire. Did you swap out that heavy flywheel for a lighter one to get better acceleration (or at least you were thinking about it??)? By putting on heavier wheels its like putting on a heavier flywheel, exactly the wrong direction for acceleration.
If you know how to calculate inertia, you can make a rough model of a wheel (a disk, and a ring), and a tire (two side disks and a ring). then you can look at the rotational energy require to spin a 14", 15" 17", and do a 22 or 24" while your working the spreadsheet. Going up two or three sizes can really take a lot more energy!!!.
So more tread = good for traction, but a 350/45/18 on a BMW with 185 Hp is probably a waste of tire.
Bigger tire means more tread, good.
Bigger outer diameter = higher gearing, more top speed (up to the limits of the engine Hp), but SLOWER acceleration.
Smaller outer diameter = faster acceleration, less top speed (did you calculate your top speed for the straight aways?? you'll probably never be able to hit max speed on any Lemons track so you don't need top speed). the shorter the track and the more turns, the more acceleration you want.
Heavier tire/wheel combination = SLOWER acceleration.
So if you want to move away from the 14", go to a 15" and look for wide rims that fit under your car. Look at the outer diameter of the tires (its listed in the specs page on most tire sites) and find the smaller diameter. maybe a 16".
Dudes Ex Machina:
https://www.facebook.com/dudesexmachina?Everyone who has ever built anywhere a 'new heaven' first found the power thereto in his own hell- Frederick Nietzsche