Hey Kimo!
I think we were the first to offer these sort of sets, and now we have 4 of them. What NewKid has (thanks for the kind words!) - the HMU-NWs (Heavy Medium Ukulele - no wound), was actually our first formulation, and the one that started things off. It was simply called the Heavy Gauge Ukulele set.
When we redid the string site, we added a bunch of new sets. In this area, we added a set with slightly higher gauges and gave it the Heavy Gauge name. What was pretty much our old Heavy Gauge set became the Heavy Mediums.
We did it because Baritones have such a wide range in scale length compared to the other Ukuleles. They go from 19" to over 20" (like our own). We had a few people with the 19" scale who wanted a bit more tension. The newer gauges take care of that. Then to top it all off, we added a wound 3rd option w/ different tensions for each set.
To sum up, I would lean toward a Heavy Gauge set for a 19" scale. For a 20" scale you could go either way depending on your desire for tension. Remember, Baritones are often built like a tank, "overbuilt" compared to typical Ukulele construction, so sometimes you need a bit more tension to get them going. The HUs will supply that. On the other hand the HMUs will give a bit crisper sound if you don't need the tension.
The wound string option goes more toward personal preference in playing style and sound. The wound 3rds give more sustain and power, both overall, but especially in the bottom end. The plain 3rds give a quicker attack.
It's a great tuning for a Baritone - you'll love it I'm sure!