Cardiovascular fitness through ski vs SUP

Thanks for the advice

Ok, good. 

Here on Maui, the main sport is outrigger.  The Tahitians and Hawaiians are kings of outrigger.  They apply skill, perseverance and discipline to outrigger by not cheating on the ama.  They push their boats to the limits of human ability. The top outrigger pros are also extremely capable in elite skis.  They cross train in skis regularly. 

So, no disparagement at all on the outrigger.  All the best paddlers on Maui are in outrigger.  

Outriggers are actually far tippier than skis, that's why they have an ama.  

But you are a beginner, so this is all academic.

Do what Ranga, Zach, Atlas and others have suggested and get a stable, beginner boat.  Learn how to paddle correctly.  If you outgrow the 'beginner' boat (which will take hundreds of hours - if you are lucky) you will be able to easily sell it. 
 
You may be surprised at how much skill, perseverance and discipline is required to learn a proper forward stroke. 

Faster skis are not faster in the hands of a novice, they are slower.  Barton published the numbers. 
That includes intermediate boats.  If you plan on going into rougher water that fact increases exponentially. 

The fun really starts when you go into upwind, crosswind, downwind.  That's where skis outperform all others. And you won't be able to do that without the power of your legs and torso.   You will be stuck on flat water in your tippy boat, arm paddling like a hamster in a cage. 

Arm paddling doesn't tax the cardio like the legs/torso, so it's a lose/lose situation.  You will need the power of the big muscles to be safe out in tougher water.   Your arms won't last and don't have the endurance or sprint power.    

"You may be surprised at how much skill, perseverance and discipline is required to learn a proper forward stroke. "
This is very true.

Like the poster intends, I use a ski for fitness paddling to offset my cycling which is my main activity. On the west coast of Florida (which has a big outrigger presence), the conditions are a combination of calm to very wavy. My 2 skis are Knysna Genius CLK and a Think EZE, both considered beginner skis... maybe the CLK is approaching stable intermediate.There is a huge difference between the Gulf and the calmer Intercostal water I normally paddle in and couldn't imagine paddling anything tippier in bigger conditions...or want to.

Stay with a stable boat and develop your stroke. Mistakes with technique are very unforgiving. Even if you have the balance for a tippy ski, poor technique will hamper your speed and cause joint injuries. You won't notice a speed difference of a stable ski since the water is an extreme variable. 
As far as boats go.... Eventhough the CLK moves through the water better, the Think has a very nice ergonomic fit for fitness paddling. You are looking at a good brand for for that purpose...consider a Think as well if possible.
 

I am convinced that I would be best served by a stable ski. I tested side-by-side a Vega Flex and more stable ski and was able to work on pointers given to me by the instructor in the stable ski. Thank you for the advice.

I have a related question about lower back issues for surfskiers. I noticed that as long as I was following the instructor's hints on using my legs, I felt that I wasn't loading up my back much. But it was a short session and I have a history of some lumbar back pain. Does sitting low relative the feet in a boat necessarily put the rower at a greater risk of lower back strain, or with proper technique and lessons, can the lower back be kept in a more neutral position, or in motion in such a way that even those with lower back issues are able to slowly build up to longer, harder distances?
 

Yes to all of your questions. Lower seats are harder on backs. If your ski is stable enough adding even a cm of seat pad will help with back strain. Stretching hamstrings and also calves and instep of the foot will help. Putting a block on the footplate where the heel touches to decrease calf stretching will help. Start easy. Gradually build strength. It will take time before you can sit comfortably in the right position. Takes me 6 weeks every spring before I feel good in the boat after taking the winter off. I have back issues - lumbar fusion and other things. As with many people with low back issues, paddling actually makes my back feel better, looser, and stronger. But you have to ease into it gradually. 

Thanks for the advice and encouragement. I went for it and got myself a nice stable ski and had a good beginner lesson. My heart was definitely pumping, but I hardly noticed because I was having so much fun slicing through the water. I will be watching my form closely and be taking it slow so I stave off lumbar spine issues and shoulder pain. But with good form, I hope to enjoy the sport for a long time.