Will I be able to applying for a 1 year marriage visa soon, and I am curious if I will be able to travel freely out of Thailand then return to LOS as I please. Are there any limits on the amount of time I can spend outside of Thailand?

There is no marriage visa so believe you are talking about 1 or 2 below:

1. Multi entry non immigrant visa valid for one year and issued by a Consulate allows unlimited travel with each stay up to 90 days.

2. One year extension of stay issued by immigration inside Thailand. Allows no travel without a re-entry permit. Re-entry permit cost 1,000 baht single entry or 3,800 baht multi entry (valid up to the permitted to stay date in your passport) and allows unlimited travel during that time with each stay being to the same permitted to stay date in your passport.

"Re-entry permit cost 1,000 baht single entry"

Are you required to apply for this at a Thai Embassy?

You can not apply at a Thai Embassy - it must be issued inside Thailand prior to any travel out. Immigration office issues them. What most people do, if they plan a number of trips each year, is to obtain the multi re-entry permit at the same time they receive the final one year extension of stay stamp.