What visa options do I have for a 3-month stay in Thailand with two separate entries?

Some people are over thinking it here but yes the no need for a visa and use visa exempt is most simple. You will fly in and then 5 days later fly out to your next destination. This trip will be your onward ticket requirement sorted - just make sure the 5th day trip out isn’t a land border crossing. And then as others have said when you come back you can get a 30 day extension to make up to your 5 weeks before you fly home. The single entry tourist visa might not work that well as the immigration officer may activate it in your 5 day trip rather than the 5 week one (unless you apply for one later).

london.thaiembassy.org/en/page/visa-general-information?menu=64cdf080d54bb16df93

As Todd says above, do you 1st t days with no hassle at all, come back on your 2nd visit and before your 30 days is up go to local immigration office and get another 30 day extension for 1900baht, bring passport photos, photocopies of your passport main page and entry stamp page, the resg of the forms tou can fill out at the office

You don’t need a visa at all. Come in visa exempt. That’s all you will need. If you are gonna pass 30 days in country, you can extend another 30 at any price immigration office. Basically you don’t need to do anything

You could get the 6 month multi entry visa too. That would also work but for the time you're staying, may not be worth it be it I don't know how much it costs compared to the 1900 cost of extension

Unfortunately you have it back to front. The other way around a 60 day TR visa would have been cool with a 30 day exempt on your return for the 5 days. The way you're doing it you could either arrive visa exempt, move to your next country and apply for a 60TR there if you have the time or arrive visa exempt, visit your other destinations, return on visa exempt and apply for a extension at your nearest immigration office

If staying under 30 days you don't need visa

No one can answer that correctly without knowing your nationality. Different countries different agreements