Don't put it in the freezer.
I don't seal the lid very tight when I place in the fridge. I normally take a whiff test of my cold starters and check for bubbles in it, after about a week or sometimes two weeks. If it smells good and is not discolored, I discard half and feed then stick it right back in fridge.. in the fridge it won't be so hungry! I keep about 200grams total of each of my different starters in the fridge.
The main reason I would have 2 jars would be to keep your backup in the fridge and keep the other on the counter that you will be feeding daily. If you don't have time or don't bake every day, maintaining your counter starter isn't really necessary...get rid of it.....but then you do need to plan on preparing your cold starter about a day before you bake to wake it up a little and be sure it will be strong nough to ferment your dough.
I personally would take one jar, feed it remove enough to start your dough formula, but place that jar in the fridge and keep a cold starter...but that's beause I struggle wih keeping a counter starter. You see it's jst like having a baby. You really need to take good care of it.
Next, I would empty part of your 2nd jar onto a clean plate or a piece of parchment and let it dry out. And then get rid of that 2nd jar unless you want to keep your counter starter feeding it every day. This dried stuff will be your emergency backup flakes that you can store in a ziploc bag or in a jar and if you need to...you will start this whole freaking process again with those flakes.... but that is only your EMergency backup. Then either keep feeding what is left in the jar ,leave on the counter and continue to feed every day to keep it alive. I'm repeating myself, but I hope you succeed with starter maintenance.
You can use your culture in any dough. You will now be falling into more experiments, faliures and success wih dough formulas. Keep at it!