We use muriatic acid all the time. The "pure" stuff (actually about 38% HCl) is super super gnarly. You should be able to find it at pool supply stores. Don't open it indoors. It releases a lot of fumes in its pure form that are dangerous, so obviously don't stick your face near the lid. Use a face shield, goggles, scuba mask, whatever, but it will blind you if it gets splashed in your eyes. Use long gloves. We don't really have any typical use for the pure stuff. It is too dangerous to work with except for special circumstances.
Once you dilute it down to 10% (9 parts water, 1 part "pure" HCl) it will be much easier to work with. You can splash it on your skin and it won't harm you. If you have little cuts on your hands you'll feel it like lemon juice, but it is not going to leave burns. To make 10% HCl, add the 1 part acid to 9 parts water, NOT THE OTHER WAY AROUND.
For soaking rocks, 10% might even be a bit much. You'll create a lot of bubbles and foam. I would start with a 1% bath (add about 1/4th of a gallon to your 45 gallon tub) and go from there. When the rocks stop bubbling you've likely reacted all the HCl with CaCO3.
To neutralize the solution when sending down a drain, use baking soda. You may get some foaming and fizziness so just be careful with it.
