In my opinion if you are going to be taking alot of gear (I freedive too so I consider two tanks to be 'alot' !) then I would go for the zodiac.
Even a little one would be preferable to a kayak for these conditions I think.
For what you want to carry you would need a stable kayak. Stable kayaks are heavy to carry and heavy to paddle - I think that you would get tired paddling any distance with this set up.
The alternative is to get a sleeker kayak.
This would be lighter to carry and more efficient to paddle. However it would be more 'tippy' and harder to enter/exit with tanks.
Plenty of people scuba from kayaks I am sure but I would still recommend a zodiac for scuba.
You can get very good advice on
www.paddling.net.
Perhaps the best thing to do would be buy a small/light plastic SOT for having fun with paddling around and enjoying the lake (I went past it once - it looked awesome in winter

) and also get a small zodiac for scuba. If you are nervous about boats then I am sure they run a beginners zodiac course near you ?
Just my opinion

(I use a Cobra Expedition [18' x 25" I think] for paddling about in the sea and wish I a faster/sleeker kayak already

)