Hi & welcome Pranahorse,
Firstly, if there are no health/quarrantine type issues with the new one, if both horses have lived with other horses before and if the paddock you have is large & open enough for them to get away from eachother & not be cornered, I'd first let them into it & explore individually, so they know the lay of the land, then I'd just let them out together & keep an eye on things for the first hour. Sooner the better.
Horses are herd animals, much healthier & happier with company. They have their 'politics' and can play rough at times - it can look scary, but barring socially deprived horses who haven't learned how to behave, and the rare true 'bullies', they very rarely injure eachother, past a few scrapes & bitemarks, and if allowed to settle, they're generally pretty peaceful animals once the initial 'dominance games' are sorted.
I plan to eventually offer private trail rides.
Lovely! But if you're new to horses & not yet very well versed, I think that 'eventually' is a very important consideration - don't rush in. Hate to say it, but depending where you're from(I don't know about Costa Rica), liability may be an important consideration with horsey business too.
on which horses she selected for that days ride, some where from one "group" or another and so got along well or did not. The competition and sometime nipping was due to horse being from her different groups.
This is a training problem IMO, not so much about different horses. All horses engage in 'political debates'
and teeth & hooves are commonly used. They generally enjoy these 'games' & it doesn't necessarily mean they don't get along(2 young boys I had recently just hated to be separated, but loved to 'play fight'...). But to be safe for riding, especially in a group, they need to be taught that when they're on lead or ridden, they're on your 'payroll'. They're not allowed to play their horsey games then. That's for paddock time. ....And then there's the bit about the horses eternally stabled except when ridden... never get to BE horses...
Of course I imagine I will allow them to meet through some bars at first, and I assume that I can move them so that they have stalls next to each other, right now they do not.
Yes, if there is any likelihood of either being unusually aggressive, getting to know eachother through bars/fence first is prudent, and if they're stalled now, yes, I'd keep them next to eachother until you can get them out.
Also, All of the horses at this barn are fed grass cut from the farm's fields, so they are already acclimated to eating the grass. Luna just got here, so I imagine that I need to acclimate her to eating fresh grass before setting her free
Do they get hay as well?(Just because sounds like a lot of work, a LOT of fresh grass would be needed for a stable of 24/7 locked up horses.) While different grasses can be richer than others, whether it's fresh or dried(as hay) doesn't make a difference, except in water content, and it's generally not something that needs 'acclimatising' to anyway.
If your horse(s) have come from 'slim pickings' and aren't used to rich feed & you have 'nice' pasture, then they may need to take it slowly - let them out for a few hours a day for the first week, then increase & keep an eye on them. If they're already overweight & the pasture is rich &/or abundant, then you may have to be cautious.