This depends on many things..
Your physical condition
the condition of the turf
If one mows every day, and twice daily during our monsoons, then the clippings will be short enough.
A reel cuts, but needs perfect turf; the rotary hacks - certain grasses are OK with this "butcher job".
Grass catchers are, or were available for reelers. I have one of these antiques, believe be, using one is a workout.
My son-in-law uses one on his 1/10 acre, but the time will come.......
I now spend more for lawn mower gasoline than I used to spend for Diesel fuel for the daily work commute(20 years ago)..

My physical condition is pretty good, so I don't worry about that. However, my turf is no putting green, and you said a reel mower needs perfect turf. Sounds like a reel mower might not be an option for me.

Reel mowers, push or power, will require more attention when it comes to mower maintenance as well as when mowing, and will for the most part, be more costly. A 1/2 acre is a LOT to mower with a push reel.

Here's a link about some push reels if you're still interested.

Here is a link that might be useful: Push Reel Mower Reviews

I used to use a push reel mower. Here are some of my thoughts.

-one comes to a sudden and jarring stop at every pine cone and some small twigs
-they are light so really aren't much harder to push than a regular gas push mower
-one does not take over untamed areas with a push reel mower
-flat blade grass gets cut the best. feathery or round blade grass doesn't cut so well.
-a string trimmer can help with small patches of disgreeable grass
-I had an 18 inch cut. I believe a 20 inch cut is now available. get the widest you can find.

You might also consider an electric mower. Without too many obstacles even a corded electric might do the job.

A reel mower would be leaned up against the wall somewhere after a couple days and you would then go buy another gas mower. Just bypass the reel and save some money.

Push mowers require regular maintenance as well. You may or may not be capable of sharpening and adjusting the mower but that is required for a decent cut. Are you really up to pushing a mower through 1/2 acre of grass? Get ready for several hours of work. It takes muscle power and is a lot slower than mowing with a rotary. I think you will find the push reel mower end up at the back of the garage unused after a few sessions.