Hi Dave,
Oh geez! There are literally dozens of cam grinds possible! And probably just as many or even more opinions about what makes for a good cam.
First of all, it is usually no more expensive to have a cam ground to be moderately more aggressive, than it is to have it ground to stock profile. The same work needs to be done, either way. It is only more radical cams that get more work at higher cost.
And, there are many aspects that can be changed to tune a cam's performance. Often degrees of duration or duration plus lift are used as a key point of comparision, although there are many other factors (overlap, symetry, lift at the lobe, lift at the valve, timing and lobe profile are some that come immediately to mind).
I would call a 270-290 degree cam a moderate improvement. I don't know what the original P.I. cars used, would suspect it was relatively mild since most of Triumph's cams were: best guess, about 260 degrees. (Carbureted cars seemed to be fitted with about 245 degree cams).
Once you get up over 290 or 300 degrees, it's more of a full race cam and has to have more work done, thus costs more, and will lose some street drivability because it moves the effective rpm range much higher (and reduces low end torque). Of course, once you get into aggressive, high rev cams, that means many other engine mods will be needed to keep it all together at those higher rpms.
Many people seem to over-specify their cams, but it sounds like you are aware of this potential pitfall.
In terms of lift you'll see some cams specs stated at the valve, others at the lobe. The rocker arms give a ratio that moves the valve farther than the lobe lifts the follower. Usually, when a cam grinder states the dimension at the valve, this is using a relatively common and mild 1.5:1 ratio (but this is a good thing to ask a grinder about). Be aware that stock Triumph rockers are really more like 1.45:1 ratio, so are conservative. That means a little less valve opening (and thus a little less gas flow). But, it's "safe", I suppose. At the other end of things, some aftermarket roller rockers provide 1.6:1 or even 1.7:1 ratios, which can lead to other problems and really change factors after the cam grind, make for unpredictable results (and sometimes broken valve springs and other nasty problems).
The point is, usually you can convert back and forth between lift at the valve and lift at the cam lobe using a 1.5:1 ratio. That's what many cam grinders use. This is often necessary trying to get apples-to-apples comparisons between cams, I'm afraid.
You'll have to do some research, chat with some folks and match the cam to other work you are doing or have already done on the engine.
A brand new cam, freshly ground on a blank, is preferable in some respects, but is a lot more expensive. The main difference is that whenever a cam is reground, there is some loss of the lower part of the lobes, too, necessary to establish the new profile. Because of this, new, slightly longer pushrods might be needed as well. (But that might be offset a little or a lot if the cylinder head is skimmed to straighten it up, or if it's milled significantly to increase compression.)
When changing a cam, I'd usually plan on new lifters (cam followers), pushrods, and possibly valve springs, as well. In your car, you will likely want to install cam bearings (just a matter of adding Spitfire bearings in TR6/GT6 motors), since the cam is probably now running directly in the block. Also, a freshly reground cam usually needs to be hardened (nitriding or similar), or it simply won't survive past the first ten minutes of running. When it's installed, use lots of cam lube to help it survive, too.
With significantly more aggressive cams and higher rpms, stronger springs are often used to prevent "bounce" or "float", where the cam follower doesn't stay solidly planted on the lobe, messing up valve timing. However, with stronger springs comes faster lobe wear. Ask around what's needed. I can only tell you that stock springs are pretty good on the 4-cyl. TRs, these engines don't tend to have problems with bounce of float, so at most only a slight spring rate increase is needed in most circumstances. It might be different for the 6-cyl. TRs, though.
To start finding out more about cams, check out all the usual suppliers and info they have on their websites. One place to start is Elgin Cams. They have lot's of cam info online.
https://www.elgincams.com/
Kent is a big manufacturer of LBC tuning parts, and might have a website. I don't have a URL for it.
I know there are some other websites with lots of info very specific to TR6, but don't know how much info they offer about cams for P.I. applications.
Finally, with an improved cam, you might want to fit an adjustable cam sprocket up front, so you can really dial in the valve timing as close as possible and get the best out of the cam. These sprockets are pretty widely for the 6-cylinder TR motor.
Hope this helps!
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