Pictures would sure help. By self-propelled, I'm assuming you mean a 36" or larger commercial mower. And with a sulky, you can ride on them. These can be very fast and productive; work well on hills. There are two kinds of "ride on" mowers AKA tractors. Lawn tractors and garden tractors. They differ by size, capability and certainly price. Depending on the slopes and the work you need to do, either can be a good choice and save time and your back. I use a garden tractor )Derre X500) because I need to pull a trailor up a very long steep grade. Most shops will pick up and deliver a tractor (for $) when service is needed. Do you have a budget?

OP - with your acreage, mowing frequency and plans for more "obstacles" (shrubs, etc.) - may want to look at an used commercial zero turn mower.
good cutting speed, tough machine. And - as already noted - a good dealer will pick up/return your machine if it needs repair...

A self-propelled mower of adequate size would be just as much of a PITA to get to the repair shop as a lawn tractor when it requires service.

I have 2 acres and a john Deere X500 garden tractor which mows and blows snow in the winter. The neighbor across the road with 2 acres is a professional landscaper and has a powered walk behind of considerable size. Takes him three times as long to mow as me and he's walking while I'm riding.

There are other things a riding mower can do for you around the house and the cost of a good one can offset over many years of reliable service.

I'd be leery of a zero turn on slopes along ditches.

Professional L&G dealers (not Sears, HS, or Lowes) will bring out hardware for you to test on your property.

I don't have three acres but a 3 year old home on 3/4 acres. I have an older JD-LT155 with a 38" mower deck. It has no problems with the slopes, in fact it surprised me when it was able to climb out of the ditch in the front yard.

While there are many solutions to the mowing problem, there are other uses for a tractor. I would recommend a tractor either one like the LT-155, or one of the heavier ones. With three acres and your desire to make additional planting, you will appreciated the tractor with a trailer to move all of the tools, plants, seeds, mulch, fertilizer, and things yet to be discovered that those flower beds and new trees will need. Right now I am looking at putting a water tank in the trailer to water those new remote plantings.

If you can afford two I would get a tractor and the zero turn.

Thank you for your input. I should have mentioned I'm on a budget. I see you guys are in the 'big league' with John Deere's tractors.
I don't have 3 acres of grass...probably 1 1/2, the rest is field. So I meant those Yard Machine 14.5-HP/38" twin blade lawn tractor. They go for 1200$ (I'm in Canada) or something similar to that lawn tractor...in that category, I mean. As for the self-propelled gas lawn mower it would be something similar to the Yardworks 173 CC, it goes for 400$

I think it might be an idea for me to try to get a better tractor later when I have the cash for it instead of buying the one mentioned above...I don't know. Maybe the self-propelled lawn mower could do the job for now. It's a lot of grass. It will keep me in shape that's for sure.

Thanks again,

Anicee

Would you consider buying a used but stronger machine? I bought a Deere GT262 four years ago. It wasn't well maintained but I was able to make it right for just a few hundred. Importantly the engine and trans were in good shape. As time has gone by I've been able to add a snowplow a snowblower a tiller a trailer and since it came with a deck I have nearly everything Deere made for it. There are other attachments but for now I'm all set.
One of the biggest reasons I went with Deere to begin with is that I can still buy new parts from the dealer for a machine that's nearly 20 years old. A YardMachine? Not so much

IMHO I'd consider something like a snapper, quality wise in a self propelled unit. Good workout and add years to your life keeping the heart healthy. As pointed out however, have you considered all the eventual uses, needs? Will you be blowing/plowing snow, pulling a trailer, big veggie garden, etc.

You mention slopes and ditches, if you get a walk behind, consider getting cleated shoes of some type for safety, also even with a rider, most folks have an old push mower for trimming and such particularly around trees and things.

Let's see, I got out of the Marines 42 years ago with a 24" waist, now it's 36" I'm sure that mowing the 4 acres with a walk behind would offset that somewhat. Nah, I'll stick with the GT....:-)

Good luck,

Ev

Thank you for your suggestions. I'm French speaking so I had to check the 'snapper' and it might be good for me. I have someone who does my snow in the winter. Of course the ideal would be to have a John Deere tractor on which I could attach a trailer for when I garden and collect garden debris etc and a self-propelled lawn mower.

Anicee

There are many lawn tractor that will pull a lawn trailer. I mentioned John Deere because that what I have. Inherited it when my Dad died.