I'm not in agreement with Mitch on the swing axle suspension. The swing axle handles totally great IF TRAVEL IS CONTROLLED. Keep the car low, and the camber near zero positive toward the negative range, and handling is good. There are various ways to do this.
1. A camber compensator bolted under the trans(usually need longer studs for this). This is a great option for Speedsters.
2. A Z-bar keeps the positive camber controlled by allowing roll in the rear suspension but NOT positive camber. This is custom fabrication and the most effort, especially tuning it, as it adds rear spring rate.
3. Limiting straps can be installed to prevent positive camber. This is the method I used on my Spyder. Camber is limited to a couple degrees positive, which doesn't allow the tire to ride on its outside edge.
4. The last option is zero-roll. This is used on Formula Vee cars(I have one) and uses one shock and a droop limiter rod to control rear camber. Not really practical for a street car, but excellent on the track in a Formula car.
A lot of people don't run a front anti-sway bar on the Speedster or Spyder. A front bar does shift the handling to neutral/understeer but the car is much more predictable. It corners much flatter. The cornering limits are higher before snap oversteer shows up.
The stock 1/2" VW bar does a little. The aftermarket 3/4" EMPI does too much. Years ago there was a 5/8" bar available(which was the sweet spot). Since they weren't available, I built my own, with conventional attachments: sway bar bushings and end links.
Do not, under any circumstances, install a rear ant-roll bar on a Speedster with swing axle rear end. Just don't.
Now, onto tire sizing.
A 185 section width should be on a minimum 5.0" rim. I run 185/65R15 on a 4.5" front rim on my Spyder. Yes, it's not recommended, but with the backspacing requirements, tires available, and wheel well space it is what it is. I run 22F pressure, no less. It works.
So a 175 on a 4.5" rim is about perfect.
On to the 5.5" rims. In my experience, you can run up to a 205mm tread width. 195 appears to be a sweet spot, with 195/60R15 on the rear of my Spyder at 25-26 psi.
I was lucky enough to get a set of Vred Sportrac5 a couple years ago for about $300. Yup, for the whole SET.
The treadwear number on those is 300. Anything higher than that is too hard. If you're looking for GOOD and sticky street tires, look for 200-300 on treadwear. That is the sweet spot. There used to be some Yokohama Direzzas with a 300 rating that Henry would put on his IMs. Similar to the Vreds, sticky, but not too sticky.
The Sprint Classic is a good choice. I think Pirelli, Conti, and maybe a couple others make vintage-specific sizes with sticky or semi-sticky offerings.
There are Avons available with a 100 rating(I think Marty had these on his IM turbo) but IMHO too sticky(and high treadwear) for street usage.
But that smoking deal on the Sportracs is a gone thing...
And for the record, I absolutely LOVE mine. Transformative, indeed, as Stan states.