We have a 27ft round AGP so we are in a similar situation to yours but we have had our pool for over 20 years. I am not a "pro" by any means but feel that over 20 years of success with maintaining our pool ourselves gives me a bit of credibility to answer questions.
When our pool was installed the contractor had the pump running to full circulation of the water and dumped in two 2 1/2 gallon jugs of chlorine - this was to accomplish a thorough shock of the tap water used to fill the pool.
There is a lot said on pool forums about NOT using stabilized tri-chlor tablets but we have used them all the years and found them easy for maintaining stable levels of chlorine in our pool since chlorine is our sanitizer of choice.
Our contractor installed a in-line automatic chlorinator into the output pvc line from our filter. It works very well and makes adding chlorine pretty easy. Going against some of the grain here our personal experience is that using tabs with a stabilizing agent is great and convenient. Non-stabilized chlorine (bleach or liquid from the hardware store) is wiped out pretty quickly by bright sunshine - we didn't want to be trying to be chemists daily re chlorine - ain't a thing wrong with using tri-chlor tabs and with an in-line chlorinator they are almost carefree.
Yeah, sometimes too much stabilizer will cause chlorine to become "bound" reducing free chlorine in your water - a thorough shock is the easy solution to that problem - in our exprience and opinion.
Our contractor gave us great pool instructions for newbies - he described our pool as a big stomach. Use your test kit to test your "stomach" - a sour stomach is a pool with low PH or Alkalinity - the cure is either sodium bicarbonate (low Alkalinity) or soda ash (low PH). A too sweet stomach means PH or Alkalinity too high requiring adding a cup or two of liquid muriatic acid until test kit shows levels are in proper range. His final instructions were to be patient and adjust PH or Alkalinity in small steps until all levels including sanitizer become in range and stable and once that is done maintaining those levels is easy with regular monitoring.
In the over 20 years since we began following that advice we have to agree.
The really good news is pool chem maintenance really isn't rocket science - there is no need to pay some "expert" to take care of your pool.
The true "correct answers" re how to maintain pool water vary - some will recommend you worry with it at some chemistry bit level - do that if you care to - using bleach instead of stabilizing tabs works just fine but we like the ease and convenience of using three inch tabs in our in-line chlorinator - but if you keep your "stomach" from becoming too sweet or too sour and have a stabilized level of sanitizer (our choice is chlorine) you can just spend minutes on water maintenance and hours and hours of swimming pleasure. It is really no harder than that.
Final - don't forget to use a good angaecide. We found that a brand that promises at least two weeks of algae blockage works best for us.
Sorry to rattle on so long - hope you don't mind - I just read the half page instructions that came with our 4-way test kit from our neighborhood hardware store - follow those instructions and you will do just fine!!!