I think Green Dean answers a lot of your questions here:
Hawthorne clan - what you can eat
The takeaway is that like apples, don't eat a bunch of the seeds, as they contain a cyanide compound. Same with many stone fruit.
Having eaten a few types, I would say pick the tastiest ones with the least seeds and biggest fruit that can grow in your region. I like to aim for the easiest to prepare and harvest that still grows well near me.
C. monogyna is very convenient as that it's hardy and has one seed. That's the one naturalized across the US, which I've eaten and harvested the most of over the years. Lots for tea and jam. Removing the seeds for jam is the challenge, but basically you have to cook them a bit and then press through a strainer. Since you have to do this with the single seeded or the native multi-seeded types, it doesn't really matter labor-wise, so it more comes down to taste. Some varieties are very mealy and not flavorful.
In the cooler regions, Chinese Hawthorn can also grow, and it's fruit is a tad bigger. But I must say that what the native hawthorns and C. Monogyna lack in size, they easily make up in production on bumper crop years. However, smaller stuff is a bit harder to pick.
Here is a Chinese hawthorn from Raintree. It's like a little crabapple.
Chinese Haw fruit
Here are recipes from Chinese cooking:
Chinese cooking hawthorn fruit
Removing the seeds:
Finishes product from this recipe:
You can see it looks a lot like little crabapples.
If you live in the SE and have a lot of moist ground, you might like the native Mayhaw:
Mayhaw varieties available from Ty Ty nursery
Here is a small Florida nursery selling wild Mayhaws and jelly, too:
Golden Acres Ranch Mayhaws and mayhaw jelly
And here is an article about mayhaws and their use in permaculture:
Mayhaw uses in Permaculture
I believe Burnt Ridge Nursery also has them seasonally.
For other warm regions there is the tejocote, or Mexican Hawthorn. It grows in zones much warmer than you- zone 9 and up. You can buy it in the US in Mexican grocers near October-December. It has a unique tropical flavor and is used for dishes including a traditional Mexican punch for the holidays.
They are very tasty, the best flavored in my opinion. But again, they only grow in warm climates.
If you want to start any hawthorn from seed, the native ones and the C. monogyna will reseed themselves rather easily. Birds seem to drop them everywhere. In Oregon I never planted any, just wildcrafted for them because they were very plentiful.
But if you want one of those with bigger fruit, I think you might try the way tejocote is started from seed commercially- you have to find a way to get the seed coat to crack. It's hard, like a little cherry pit. I found directions that worked, finally! Clean them off as much as reasonably possible, then soak in water a couple days. Then let dry. Then soak again. Repeat until the hard shell cracks open. Then I was able to dry them and keep them refrigerated over the winter. I planted them in a pot in the greenhouse as it warmed up, and they sprouted in about a month.
And I almost forgot Azarole! That's one from the Mediterranean, USDA zones 5-9, I believe.
Azarole, the Mediterranean Hawthorn
I love how much variety there is in Hawthorns, like the poster has pointed out. A hawthorn for almost every landscape and climate. And I like how loved they are through the world, the temperate and sub tropical. One of the old foods. I hope you find some you like!