Good answers everywhere here, especially Cheseroo's.
I'd add (and then get on my soapbox): The first two things that you are racing against are (1) your own ability as a team and (2) your equipment.
Lots of people get wrapped up in what others are doing in Lemons; you need to run your own junk first and only after a few/many races should you even trot out a measuring stick, assuming you care. And it's perfectly acceptable--encouraged even--not to care about the actual race(s) going on.
I'll recommend that you Keep It Simple Stupid (K.I.S.S.) for as many races as you can and don't try to upgrade 800 things at once. Run the car as stock as you can for a couple races and don't abuse it. Don't rev to redline every shirt and threshold brake every corner. Lemons is old-school endurance racing: Take care of the car is Job #1.
If you feel compelled to change anything, improve one thing at a time so you can figure out if it actually helps or tinker with that one thing to make it more effective. Don't modify the car in a way that can't be undone easily.
This is also a long game: The driving ability and car capability tends to grown incrementally over a long time.
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On a technical level: Fiat = No Penalty Laps, pretty much. True of most Italian, British, and French things. Other stuff really depends on how much it seems like a Real Race Car™ with Real Racers™ running it..
On the Fiat, if you put a "reasonable" swap into a Fiat like an Ecotec or even a Ranger 2.3L engine, it's going to make far more power than it was designed for. You'll still have the chain of related failures (brakes, tires, probably cooling, differential beefiness, and fuel tank capacity/feed) that you will need to sort over several races. That doesn't mean you shouldn't do it, but it's a much harder path.
Small-Block Chevys (and most pushrod V8s...and most Lemons engines in general) do not like revs. High RPM kills Lemons engines. If you've seen this post, that is a team with a Small-Block Chevy. Subtract 1000 of the factory redline, at least. All you're doing is burning extra fuel and creating A LOT of eventually-failing rotational momentum at 5000 RPM.
Hondas are kind of the same story. Lots of revs will toss rods. Purge and flush the coolant system well before you race. Have a set of head gaskets on hand and dog-ear the head gasket page in the Haynes Manual. Like all FWD cars, wheel bearings are a wear item and you can have a set of half-shafts in the boxes from the local parts store with a receipt to return it after the weekend if you don't use them (though there's a good chance you'll use at least one of them).
Whatever you build or buy, run the highest-quality brake fluid and a set of endurance racing pads.
Eric Rood
Everything Bagel, 24 Hours of Lemons
eric@24hoursoflemons.com