I have 3 Glaviz Devices, and 2 Spheres of the new Era. So I have 5 chances to change my race for free (and I don't plan to spend money for this).
I am an Inergon Builder rank 311. I'm pretty comfy with the energy bonus, and I don't think I'm ready to leave the Builder Profession for long... given the upkeep on my modules. However, I would take on some cheaper modules to use in the short term to fulfill medal requirements.
What is the best strategy for changing races for getting medals? Are there some key races I should switch to in any particular order to take advantage of medal opportunities?
I'm mostly just trying to avoid using these race/profession devices, and regretting it later.

Your going to have to spend GP on changing if you want all the medals.

Technically you don't, as you can gain 2 more spheres of the new era each year, it may take 4 years, but its possible. Highly unlikely yes, but you dont need to spend gp on changing for all the medals

but you will for mission planets, father, trinity cores etc.

You could also use paradox generators on new years to get quite a few spheres
Whether that is a good idea is a different question.

You can get three each year, if you time your New Years Eve and New Years Day collections correctly.

Unless I'm mistaken, in addition to the daily reward medal for the initial races and the NI medal for the unlocked races there's also a medal for every unlocked race also has its own medal that is linked to its specialty/ability. So if your goal is to get all the medals you'll have to hit them all.

viewtopic.php?f=4&t=24692

This thread is a little out of date and missing a few races, but otherwise gives a good layout of quick ways to get medals.

more if you plan on a series of invasion during the period which might lead to paradox usage.
thou i'd suggest against using paradox solely for spheres. I'd go on a scan run right before and pick out a few reasonable targets.
also suggest a supply of annex decree for between successful invasions to minimize paradox wastage.

I didn't know about the 2+ spheres with the right timing... Good call! This is exactly the info I was seeking, so thank you! The above link to the race changing page is a great outline for what I want to do. I might change the order up, but this gives me some structure so I know how to juggle these races. Ha. I'll have to look up the paradox device. I've heard of it, but have yet to discover its uses.

paradox generator is a super TM that also reset invasion timer and daily gift.
the primary purpose is for the invasion timer, but if it can overlap with a sphere daily it's all the better