Hi,
It's a tough question. Wire wheels look great!
The TR3 came with either 48 or 60 spoke wheels, didn't it? If I were considering wire wheels, I'd prefer the later 72 spoke (TR6), just for the strength. These are wider, too. The 60s were a little wider than the 48s, too. All the wire wheels tend to be narrower than the steel wheels used on the cars at the same time period, though. It might be tricky to find good fitting tires for the narrowest wire wheels.
I have the Panasport copies of the Minilite wheels you mention and I really like them on my TR4! IMHO, they look great on TR3s, too. There are both bolt-on and center-lock versions of these wheels, so you can enjoy the knockoffs, or not, your choice. The knock-off versions and their hubs are significantly heavier. But, they do look great!
Unsprung weight really effects handling. Aside from the solid rear axle housing, the largest contributors to that on these cars are the wheels. Bolt-on Minilite or Panasport are the lightest, unless you track down some magnesium wheels (rarer and older, used ones need careful checking for cracks). Next heaviest are the stock steel wheels. The heaviest of all are the 60 and 72 spoke wire wheels, especially after the necessary hub adapters are added.
Wire wheels with their adaptors do make for a slightly wider track both front and rear, which is good for handling. Of course, the same can be achieved with some wheel spacers behind any bolt-on wheel, if the wheel well allows enough room.
If originality is an issue, silver painted spoke wheels were usually fitted, weren't they? Chrome spokes were not generally offered?
I've heard really good things about Dayton wheels, in particular. They are now being made overseas (India maybe), but quality control is said to still be at a high standard. I must say, though, I've not had any personal experience with these wheels other than admiring them on other folks' cars. As a rule, I believe the Dayton wheels seldom need truing when new (but should probably be checked anyway, just in case) and hold their true for longer than most. Most other brands require truing before initial use and should be checked with some frequency by someone who is familiar with wire wheels.
The Panasports I'm using are reportedly extremely strong, too. Since they closely mimic the Minilites, I'd assume those are too. The Panasports are very popular with vintage racers and I haven't ever heard of one failing.
Enjoy your TR3!