Here are the recommendations of the American Heart Association:
Total cholesterol less than 200HDL cholesterol at least > 40, ideally > 60LDL cholesterol at least less than 130, ideally less than 100Triglycerides less than 150
Having a triglyceride range over the recommended value of 150 increases your risk for heart disease and may be linked to other conditions such as obesity, metabolic syndrome, poorly controlled diabetes, etc... It is known to also contribute to atherosclerosis (hardening or thickening of arteries) - which increases the risk of stroke and heart attack.
I've attached an article discussing triglycerides even further:
Triglycerides Why They Matter and How to Lower Them
After being on a steady treatment plan, it is typical, depending on the physician, you would recheck your lab anywhere from 6 weeks to a few months.