Home canner here:

It's not a great idea to re-use commercial food jars for home canning. You are correct in that you must use 2-piece lids for the home canning process, and the jar must have one of the two correct diameter mouths and the correct threads to engage with the ring. Most pickle jars have multi-lug lids (you only have to turn them a fraction of a turn to release them) so they aren't compatible.

They're also not meant to withstand the rigors of repeated home canning. Assuming you have a jar with lids compatible with Ball lids, you'll notice they're thinner than canning jars. They're more likely to break during the process.

Finally, heat penetration is a factor. The size and shape of canning jars is important, processing times are calculated to guarantee the entire contents of the jar have reached a high enough temperature for long enough that the contents have been sterilized. Commercial jars may not conform to those size or shape standards, so especially with solid foods like fruit or vegetable slices you can't guarantee the entire batch has been preserved in strangely shaped or sized jars.

Canning jars are widely available and inexpensive, just buy a set.

Re-using them for leftovers like tupperware is perfectly fine; I actually use salsa jars to mix wood finish in instead of buying the buckets they have for that purpose at the hardware store.