You are right the correct answer is test before and if there is an issue that requires shocking after shocking.
The test before and after shocking do not have to be the same. Before you should test for pretty much everything, bacteria, lead, arsenic, ph, nitrates, total dissolved solids, uranium, fluoride, manganese, radon, and probably a few other things I am forgetting off the top of my head. (Many of those it is recommended that you have checked on an on going basis some yearly and some every 5 years.) A couple more specific items, if you live in an area where road salt is commonly used you might want to check for salt intrusion and in some cases you may also want to look for petroleum products.
Only the bacteria is capable of being addressed by shocking with chlorine (and most wells are fine). So if you do need to shock you would only need to retest for bacteria. You'd also want to look for obvious sources of bacterial contamination and correct them (things like a missing or damaged well cap). Personally, if bacteria was positive I would test immediately after shock to ensure the shocking was successful and some period of time later (say 6 months) to ensure that there is not an ongoing source of contamination.
All of the other type of contamination are going to require some form of treatment to address. That could be things like filtration or aeration.
While not a contaminate I would also make sure to get the hardness of the water tested.
270 is high, here are the prices of a Lab in my state.
Standard Test - $65.00
Total Coliform & E. coli Bacteria, Nitrate, Iron, Chloride, Manganese, Hardness, pH, Sodium
Standard Plus Arsenic Test - $90.00
"Standard" test as listed above plus Arsenic
Comprehensive Test - $125.00
Total Coliform & E. coli Bacteria, Nitrate, Nitrite, Iron, Chloride, Manganese, Hardness, pH, Sodium, Arsenic, Fluoride, Copper, Lead, Conductivity, Alkalinity
Comprehensive Test Plus Radon - $150.00
Comprehensive Test Plus Radon
While the cost might seem high, especially when you have to run the test a few times. Consider it part of the cost of acquiring the property, like purchase price, inspections, title insurance, taxes, recording fees, and the like. Then consider the periodic tests part of the ongoing expenses like maintenance and utilities; in fact just think of it as your water bill.
Edit: That same lab charges $25 for the Total Coliform & E. coli Bacteria test.