The most important question is: for what? Are you just looking for screening?
The problem is that if you are not looking for a specific symptom or condition, you can get yourself really confused and scared due to the statistical up and down variability that all blood tests have. I'm a pathologist (doctor of lab medicine) and we have over 3000 tests in our menu!
Normal ranges are based on 95% probabilities which sounds great until you think that 1 out of 20 random variables will be out of range, just randomly. If you do 20 blood tests, it's real easy to get false elevations or depressions of values that are just flukes and then you're signed up for a bunch more testing. These are called false positives and false negatives and ALL lab tests have them.
Heart screening: get a complete lipid panel and pay the most attention to HDL and triglycerides. Total cholesterol is not worth much; it is statistically a poor predictor. Oh, C reactive protein to measure inflammation is also a good one to get. If you want a higher level screen, more money, get an ApoB or a LDL-p particle count by NMR. (in US.) They also do a big genetic profile for cardiac risk that only needs to be done once in your life. For a good lay introduction see Cholesterol Clarity by J. Moore.
Get blood pressure checked.
Thyroid: TSH is usually a good screen unless you have some thyroid symptoms; check with your doc. Thyroid disease is common but less common than the scams that have come up around thyroid disease which gets blamed for everything.
Liver function tests are probably a good idea to get every once in a while; hepatitis has good treatment now. ALT, AST, Alkaline Phosphatase, Bilirubin.
Hgb A1c measures the average blood sugar over several months and is a good test for diabetes which is epidemic in this country.
CBC, complete blood count, has a lot of complex information but is probably worth adding.
Hormones? They vary a lot through the day, menstrual cycle, etc. See paragraph above: what question are you looking to answer?
Cancer screening: women get pap smears annually unless recommended less frequent. Paps are the single most successful cancer screen ever devised. Also ask your doc about mammograms.
Everyone get a colonoscopy; ask your doc. Most people start at 50 unless you have family history. Stop smoking yesterday!