Old school versis new school.

While the diameter and width are close between your two examples, the 15" has a 5.8" sidewall and the 18" has a 4.5" sidewall.

That extra 1.25" of sidewall can be a positive or a negative for the 15" combination.  For an endurance race, it can be good because more sidewall means you can run over more stuff (curbs, bumpers, mufflers, corner worker stands, shrubs, etc) without upsetting the car or damaging suspension components.  But, less sidewall gives you better steering response.

I've always found that you can get a much lighter wheel in 14-15" diameters for a LOT less money than an equivalent 17-18" wheel. 

But, for Lemons... don't overthink it.  Cheap wheels.   Good tires.  (search the forum, there are a handful of "good" street tires to choose from amongst all the crappy ones)

I can use Corvette wheels and tires.. same bolt pattern on the Jag. need a spacer, longer studs, and slightly larger locator all simple work on the lathe.
There is a positive embaressment of riches when it comes to wheels and tires..
For Example I can buy real mag wheels (Magnesium, not just aluminum wheels, tons lighter)  and 95% tires for less than the tire alone would cost..
In a lot of junkyards aluminum wheels are worth little more than scrap value and the tires are freebees. (they normally have to pay to dispose of them)
  My thinking is while the steering reaction is faster on a 18-20 wheel, with low profile there is far less compliance which means even with a similar diameter  the contact patch will be bigger on a 15 inch tire than a 20 inch tire.. Steering reaction isn't much on a race track.. maybe in autocross but look at Formula1, INDY, and NASCAR which all work on 15 inch tires.
OH while the wheel is lighter with a 15 inch rim the tire is heavier so the package weight works out similar with a 18-20 rim/tire combination.

I'm sorry but I really have a preferance for junkyard tires..  for $50 or less I can by a tire with at least 90% of original tread plus examine them closely for damage etc. Tires that cost over $300 each new
The loss of 10% or less of the tread through wear is a reasonable trade off.. brand new tires do wear out rather fast compared to tires that have some use..
  When I race vintage tires I use them for one session and then take them off untill the next event. That makes the tires last a full season plus and while there is some minor loss of performance with cycled tires. I have used tires green and find out they are so badly worn after one weekend that I need to replace them every weekend.. If I race 6 vintage events in a year that could cost me over $5000 for the season.. Or I can spend $850 a season..
To me it's a no brainer..
  New tires look to cost around $200 each for the sizes I would use for Lemons.. That's an additional $800 entry fee.  In an event where if you drive to full potential you are likely not to finish..  Used tires would cost me about $200. Now perhaps the additional $600 isn't critical to others but I'm simply too cheap..
   Powerful cars tend to eat tires and I wouldn't be surprised if a set of them wouldn't last a full weekend..
    Incidently I'm in very good company.. Old Yellar used to raced on recaps against the might of Europe.. Tires that drove on the road raced and then drove home again.. Recaps that cost $11.00 each..

The Junk Player Special VW Jetta just finished it's 3rd full 24 Hour event entirely on junk yard tires.  In 72 hours of racing we've had one tire shift a belt. Thats it. The rest of the time the tires have performed flawlessly.  We prefer tires that are 'aged to perfection' because they last longer than 'sticky' tires.

We're running Sumitomo HTR200s in 225/50R-15, and after one race the tread is still like new. Then again we only did 106 laps on a 1.4 mile track, so that's only about 150 miles.

Why steel wheels?  Aluminum are so much lighter.  If you shop the later Corvettes they actaully offered a real Magnesium wheel that's insanely light. In fact I have my eye on a set of them if I decide to go to the taller rim. 

  Well I've raced on tires too narrow for the rim if you run a little higher tire pressure other than mounting them you shouldn't have a problem. IF you do I suggest you get an old timer to show you the tricks.
I hesitate to advise you on your options because every car is differant and responds to differant tires.
  people running light hondas etc.  need a softer tread compound while heavier cars like my Jaguar will wear them out too fast and require a tire change. 
Several of my thunderboomer buddies (Corvettes and Cameros) can only afford to race NASCAR take offs. They get a deal on tires used in qualifing or only for a few laps, read the sidewalls to make sure all 4 compounds are the same.  (Virtually every track has a differant compound and a differant compound on the left and right side.) Nascar gets a couple of laps and they get a season out of them.
When NASCAR was going to do road races in the rain they had to make 40 bazillion rain tires for the cars and  then they were never used.  So more than a few buddies have NASCAR rain tires that are brand new.

'Cause they're cheap.

Going from 215/70R-15 to 225/50R-15 shortened the tire by a full two inches giving us better gearing, lowering the car an inch, and easing the strain on our brakes all at the same time. Easy money!