Assessing what biomarkers are required for MTHFR or methylation issues depends on so many different factors. It can be incredibly complex, so it's crucial that you see someone with specialist knowledge and training. 
I start with a thorough, comprehensive case taking to assess a person's diet, nutritional status and lifestyle factors – as even low water intake can affect this gene expression. Getting these fundamentals in place is a vital component of treatment.
Genes are like light switches that can be turned on and off. Just knowing that the MTHFR SNP is present doesn’t tell us anything about how it’s actually affecting the person. Gene expression can be affected by factors like heavy metal exposure, trauma, chronic stress orillness, poor diet and nutritional status, obesity, sleepdisturbances, sedentary lifestyle and of course other gene mutations.  
The first step in the methylation cycle involves converting methionine to SAMe which requires adequate protein levels to support methionine. Sometimes I start by evaluating a person’s overall protein status from a Complete Blood Count. Protein is broken down in the body into amino acids and many are involved in or support optimal methylation. Often when a person has digestive issues or poor diet improving their absorption or dietary intake of protein is necessary before introducing any methyl-supplements.   
In general the more common biomarkers to assess initially are active B12, folate, homocysteine and as already mentioned Complete Blood Count, which covers protein status, liver and kidney function. I also assess the health of the red, and to a lesser extent, white, blood cellsto determine whether there is microcytic anaemia suggesting low iron; or macrocytic anaemia, which may indicate B12 and folate deficiency. 
One issue I often see is high-unmetabolised folate in the blood (from a serum folate test). This can indicate that the folate isn’t being broken down in the body, potentially due to either high folic acid intake or MTHFR mutations or both. The issue here is that high blood folate may impair the uptake of folate in the cells, which leads to a deficiency of folate and potentially B12.
If a person has digestive issues I may order tests for iron zinc magnesium and thyroid function. Sometimes I work with digestion first as methylation cannot function effectively with chronic digestive issues. Parasites, bacteria or fungal overgrowth, dysbiosis (imbalanced gut bacteria), leaky gut or problems with the actual breakdown of food either form poor hydrochloric acid or lack of digestive enzymes all need to be addressed as a priority.
Stress impacts methylation so addressing adrenal function, magnesium and zinc status can be important. Stress depletes these vital nutrients that are cofactors in many of the methylation pathways.
I also consider functional testing which includes a methylation status profile and DNA testing or genetic testing to look at some of the other important SNPs orgenetic mutations also involved in and impact methylation 
As you can see: it's a long list of tests and factors to consider. The answer is that it really depends on what's going on for the person in front of me. Testing is expensive so it's essential to prioritise what's actually needed. So it’s not just the status of the gene that I am interested in it really is how that gene is expressing, and if it’s expressing, how it’s being activated. This is the heart of my approach; to identify and treat the underlying cause of people’s symptoms.