Sulphuric acid is more plentiful than you might guess. In the past I have bought a small bottle from Sears Automotive. They don't want to sell it you directly - you need to tell them something like you have a motorcycle battery that needs topping. If you find battery acid, it is usually around 20% so, "do what you ought'a, add acid to watawh - cut it in half. You may also find concentrated sulphuric acid at your local Ace hardware being sold for drain cleaner - I got a gallon that way. Look for the bottles that come in an extra poly bag with those jolly roger labels. Once you have it, you can keep it in a plastic tub or plastic container - the ones that seal are nice - I saw some perfect ones at Office Depot.
I have not used Sparex, but yes it should work fine, but a little slower, and a little more expensive, and yes, safer. My comments about copper plating out relate to a used bath. As you clean scale from copper and brass, the solution turns bluish from dissolved copper sulphate. If steel or iron is put in the bath, copper will plate out on the steel. The rate of plating for stainless steel is so much slower, that this is a useful test for stainless vs ordinary steel. With stainless, even though you may not see it, copper is getting deposited, and this is the reason the second attempt for soldering always works well - the pickling and plating really prepare the surface. Pickling the joint for 4-8 minutes is typical. Less if it starts out hot, but don't put it in the bath until it will not cause boiling. Before I had an IR thermometer, I would touch the metal with a wet toothpick to see if it was above boiling.
A pickling bath cleans the black cupric oxide (scale), but not the reddish cuprous oxide that forms at lower temperatures. However, scrubbing lightly with a brass brush under running water will easily remove the cuprous oxide. You can mix baths that have hydrogen peroxide which will oxidize and remove the cuprous oxide, but I do not recommend the casual user go down that path.
I do not recommend you use any form of hydrochloric acid (muriatic acid). It will pickle the joint, but having chlorides around stainless or your shop is not a good thing.
Needless to say, wear eye covering. I get away with using tongs instead of wearing gloves. Have some means of rinsing off in a hurry if you have an accident. Also, have some baking soda handy to neutralize and clean up any spills.