First Priority mutations: Unfortunately, 23andme is not testing SHMT any more, so I can't tell if you have that. You don't have ACAT or CBS issues to deal with. So unless you have gut issues, you can probably dive right into MTHFR. If you do have gut issues like leaky gut, then treat that first. You could try some folinic acid to see if that helped (SHMT being one of the "leaky gut" genes, and folinic being the workaround for it).
Second Priority mutations: You have a double mutation for MTHFR C677T, which is the major one, so definitely some methylfolate for that. Like Valentijn mentioned, it would be a good idea to avoid "folic acid" which is commonly added to supplements and foods, especially grains, cereals, and breads.
You only have one B12 mutation, which one of the minor MTRRs (B12 recycling). You may or may not need B12 supplementation. This is where you would want to go by symptoms or functional testing to see if you really need B12. Having metals such as mercury or lead could also lower B12, and may make supplementation necessary at least until the metals come out. This is a good article on B12 deficiency and risk factors for it:
http://chriskresser.com/b12-deficiency-a-silent-epidemic-with-serious-consequences
http://chriskresser.com/b12-deficiency-a-silent-epidemic-with-serious-consequences
For your COMT/VDR combo, which is the second most sensitive one, Yasko suggests hydroxycobalamin and adenosylcobalamin. If you took methylcobalamin, or otherwise get too many methyl groups, you may get mood swings, as you've already reported. So low and slow is the way to go.
23andme doesn't report one of the BHMTs any more. Usually if you have a couple, you would have all three. BHMT is the secondary methylation pathway, so Yasko suggests some sunflower lecithin to get some TMG for that. That's another methyl donor, so you would want to take it easy.
For VDR Bsm, get your vitamin D checked and supplement if that's low. For the MAO A, Yasko suggests waiting until you have the rest of the methylation supplements on board and working well, then if you're still having mental health type problems, to add small sprinkles of 5htp (for serotonin).
Be sure to read the "Start Low and Go Slow" and "Roadblocks to Successful Methylation" documents linked in my signature before beginning.