Wellcome,
Some random thoughts:
Your budget is probably on target. You might want to invest a bit more but you're probably around entry, considering I have not priced equipment lately..

I'm not sure of the designation of the ESAB torch I have, but it's a nice little performer for welding... it was, I think, called an aircraft torch and is their smallest. It may be carrying a Prestolite brand now, I'm not sure. When I was 9 or so I got a small Craftsman cutting and welding set I still use, allthough I dislike the "feel" of the original regulators.

When selecting your cutting torch be sure not to oversize your tip. Too large a tip will give slaggy cuts, and many cheap outfits seem to want to impress you with the thickness they will cut, so consider the thin stuff. The 2" may be a little tough... how little is "here and there"? Just be sure to find a properly sized tip that's available for your set, even if it's at additional cost, if you want a good, clean flame cut to be proud of. Of course the welding tips must also be properly sized for the job as well.
(fuel consumption of the largest tip is the basis for calculating your tank size- it's usually a cutting tip)

I think more preheat jets on the cutting tip is better than less when all else is equal. (preheat orfices surround the O2 orfice on the face of the tip- a size "0" tip with six orfices is probably better than one with four)

As long as the set can maintain a steady flame, is comfortable to hold, balanced, and the adjustments dont get in the way of glove-cuffs and the like I personally think you will not find much difference between brands in occasional use. Regulators should fit close enough to the tanks to avoid becoming their own hazard; smaller sized are probably more appropriate for the smaller tanks. Single stage are suitable, and I prefer each regulator to have two gauges on it to indicate both gas [pressure] in the tank as well as pressure at the supply line; steer clear of the really cheap ones with no gauges- unless my eyes were deceiveing me they do exist.

One thing I am called upon to do from time to time is carefully (that's spelled "with care") chuck a torch in a small vise when working alone. If it's design will accomondate that, it may be a plus. I'm probably breaking a safety rule doing so. The mixing body is hollow and fragile; I like to clamp on the nut which holds the head to the body and I like that nut to have parallel sides (rather than knurles like my Esab, or something else)... with the body properly supported it's difficult to get the head to loosten unintentionally, so the hazard is to some degree abated.

I think you'd be happy with a "B" tank, but size the O2 larger proportional to how much cutting you plan to do. My tanks are exchange, so frankly I wind up grabbing whatever [small] size they have on the dock at the time. As I age and decend into decrepitude I am beginning to really like the idea of "smaller and lighter" at a level I did not have at an earlier age.

Harris, I'm told, made the Craftsman set I got when I was a kid. Victor, Prestolite, Esab are good names also, and Generico toots their own horn pretty well although I have no experience with them. I'm sure others will offer equipment advice based on experience and mention any brands I forgot.
If we're lucky Lawrence or others may shed advice on how to couple more than one small fuel tank for occasional heavy cutting needs, if thats the kind of thing you may want to do, and one can make a better argument for keeping back-up tanks on hand if one has ever run out of a gas, after hours, in the middle of a job, just when it was "clickin' along". They use those manifolds all the time, although I never had to.

Regards,
d