You shouldn't have any issues getting a non-O visa both times. That will let you get yourself setup for success on your 2nd entry.
Make sure if you didn't get married in Thailand that you get everything you need to register your marriage in Thailand before you leave. There are things you must get done in your home country before traveling or you won't be able to register the marriage.
First of all, there's no such thing as an exit visa. There's a re-entry permit, which you would need to purchase if you don't want your permission to stay stamp in your passport to become invalid when you leave Thailand.
A re-entry permit does not give you any extra time. When you leave, the date on your permission to stay stamp remains the same, and you would need to be back before it expires in order to apply for an extension.
So if you arrive in February with a 90-day non-O visa, your entry stamp will give you permission to stay until May. If you leave between February and May with a re-entry permit, you would still need to be back by May to apply for your extension or your stamp will expire.
You can either apply for another non-O when you're on your trip, and then wait 45-60 days after arriving again in June to apply for the 1-year extension. Or you can arrive the second time as a tourist using visa exempt, and then apply to convert to non-O visa at your immigration office since you'll already have a funded bank account.
Visa on arrival is where you apply for and pay for a 15 day visa at the airport. You do not even qualify for that, so I assume that's not what you're asking about.
You're likely asking about visa exempt, which isn't any visa at all. It means you're exempt from needing a visa and will receive a 60 day free entry stamp.
It's currently 60 days and has been since July 2024. No one can tell you what the future holds, but it doesn't matter that much as you could just apply for a tourist visa online if you need 60 days, or apply for a 30 day extension at the immigration office.
If you are talking about 100% legit, then no, you must attend in person. An agent can assist you, and get you to the front of the line etc, but you must attend in person and have your photo taken. Any other method involves the agent using their connections to get an extension through abnormal means.
Unless an agent is just walking you to immigration, they will take your passport and return it after the process is over with your stamps inside.
Every immigration office in Thailand has their own policies. The only place to get the true information will be the immigration office in your province. The information from any other office may not be applicable to you.