I'm getting my stuff done now, and with my crappy insurance, I may as well not have insurance. It's awful.
For lab tests? Call around. I found my Metabolic Panel at Any Lab Test Now for cheaper than other locations, all my other labs were cheaper at a local hospital. Except HIV- found that free at a clinic, as well as urinalysis testing for Chlamydia and Gonorrhea, all free.
Vaccinations- I had MMR and Varicella covered already. Got Tdap at a county health clinic, getting Polio Booster at a university travel clinic- check to see if your school/the local university has one. The one in my town looks great- polio booster for $45. Be prepared to show people the polio booster page, they'll say that only kids get it and that you don't need it.
Dental- with my normal dentist, thankfully insurance covered part of this. Still had to pay for xrays (too recent for insurance to pay again) and that proby thing they have to do with your gums. Tip- if you're not good at flossing, make a concerted effort to do it every day for a couple weeks prior. They'll have to stick a tiny probe into the space between your teeth and gums along every tooth on both sides. It sounds painful, but it's so much easier if you've been doing your flossing regularly.
Physical- Insurance didn't cover this (I swear to god, I wish the ACA was coming three months sooner. I would have saved HUNDREDS of dollars). I'm getting this from the university travel clinic for about $65, and the pap smear will cost whatever the lab charges to process it.
All in all? Be prepared to spend HOURS calling around and comparing prices if your insurance isn't awesome/if you don't have it. Call your insurance ahead and ask if they cover lab testing, vaccinations (be sure to specify if you're a dependent over age 18, this can affect whether they cover it), pap smears (if you're a woman), doctor visits, etc.
And yeah, it gets expensive. I'd guestimate that it's going to cost me about $600 by the time I'm done: $50 metabolic panel, $190 for other labs besides HIV, HIV free, $50 for Tdap administration/vaccine, $45 Polio booster, $150+ for dental x-rays and proby thing, $65 for physical, god knows what for pap smear, $30 for hepatitis C repeat test (borderline neg result? idk). And that's with (shitty) insurance, and my teeth were fine/didn't need fillings or wisdom teeth surgery.