I had the same questions when going from .25 acres to 60. Overwhelmed was an understatement. It takes time to set perspective and really figure out what you want to do and what equipment you want assuming money plays a factor. Sounds like you have a good start at the property with a ZT and side by side to plow.
The suspension seat is cheap and only going to make the rest of your mowing easier. If you add up the time you'll be mowing 6 acres that makes good sense either way and there are no wasted funds or regrets. It may be enough and you are done.
If you were to get a pull behind mower for the side-by-side and end up getting a tractor down the road, it would be better to go tractor and some sort of mower/cutter/flail and you have a semi-wasted purchase and one more thing with a motor on it that needs maintenance. Honestly, if I had to do it all over again I would have just gotten the tractor I needed upfront, and built around it over time. Then any implement you buy is sized for your tractor and application.