Plating people have experimentally determined that the addition of the appropriate concentration of ammonium chloride is needed for proper zinc plating. Following the recipe carefully is an important first step, you can make slight changes later if you feel like reinventing the square wheel, just to prove it doesn't roll.
Controlled wattage is a prerequisite for proper plating. But it isn't the entire answer. I previously worked for a plating bath company, and a plating assay was one (ancient and now mostly superseded) quality control technique. A carefully polished, flat, clean, piece of metal, immersed in an acid copper solution, held at a fixed wattage, will produce a bad plating of copper. That's not a joke. We wanted a sample to produce a bad plating, not terrible or flaking off in chunks, or not plating out at all, prior to shipment. We knew that, to achieve a proper metal plating, the end user would add an abundance of organic modifiers. You're lucky to have found an online source for zinc plating solution that is so simple.
Regarding the toxicity: HCl produces a toxic vapor, as soon as you open the jug. It reacts with pure ammonia (where're going to get that, clear household ammonia has detergent added) so rapidly, that it happens in the air above the respective jugs, producing a white smoke of NH4Cl crystals. You shouldn't breathe those. When you drop the zinc into the HCl, the bubbling hydrogen will spray the HCl out, so you'll have to watch that. By the way, you're sure there's no open flames in the vicinity, right? Having mixed the chemicals, you'll have to dry that to crystals so you can weigh them (you already own an accurate gram balance, right? No point in starting to follow a recipe you can't do accurately.) Anyhow, how will you dry them? Hot plate or oven? There will likely be an excess of one reactant or another, so something HCL, or ammonia, so those fumes will be present. A little tip, NH4Cl sublimes (look it up) so you wont want to heat it to dryness -- even though you'll need it dry in order to weigh it accurately.
You see, you mentioned the "bog standard garage", not the laboratory with fume hood or even the well ventilated work shed. So I'm letting you know what you're in for.
If I had to plate something homemade with zinc, I'd dip it in molten zinc. At least there's fewer variables.
You asked if the impurities will stick. That is correct, if the recipe is wrong, or the wattage is wrong, or the temperature is wrong, you will get inclusions. Likewise if you use bog standard "drugstore grade" chemicals, instead of plating bath grade chemicals. A textbook on plating chemistry will help you learn what to expect. It's not at all uncommon for people to take this up as a hobby, there's a lot to learn, and it must be satisfying to achieve it yourself.