#1 on Dwight's advice. Keep it simple. To use an analogy, tuning skis is like tuning up a car, and the work involved can range from doing an oil change to prepping a Formula 1 car for a race. Most people just need an oil change. Eventually, when you're underneath the car, you'll start pushing on the belts, wondering if you can change the brake pads, etc., but you don't need to start out doing that. I think many people in this forum have lots of experience tuning skis and their "basic" tuning technique is well beyond an oil change.
Before I get into changing the oil, to answer your original question, don't worry about a base cleaner. You can get most of the crud out brushing and waxing, and unless you're using spendy flouro waxes or chasing fractions of a second in a race course (doesn't sound like you are), they are overkill and can do more harm than good.
Now, onto the basic oil change. Recreation skis benefit from three things: 1) a reasonably flat, clean base, 2) edges that are reasonably sharp and consistent, and 3) wax. Establishing a good base (item 1) is tricky to do when you're new to tuning, and even many expert home tuners would rather not tackle it. The second and third things can be dead simple for a home tuner. My advice is take the skis to a good shop for base grind and have the base edge bevels set. Using a good shop is key--results can vary spectacularly! From that point forward, your job is to maintain the shop tune while doing no harm. Harm that is difficult to undo is applying too much heat to the bases, being super aggressive and careless with edges, and letting the base dry out or oxidize from not waxing frequently enough.
I started out doing edges and wax without even vises. But that's a pain in the ass, so get some vises and mount them on a solid bench. Then get an edge guide and a 100 or 200 grit diamond stone. Regularly touch up the side edges using the edge guide. Use a light touch (pushing hard will distort the angle between the guide and the diamond stone), take your time, and work the whole length of the edge consistently. For the base edge, I have angle guides, but for the most part I eyeball it and only touch the base edge to remove burrs. Congrats, you're now done* with edges!
*Note: as with all things, you can take your edge work to the nth degree, and before too long you'll be pulling sidewall, working your way up to 2000 grit arkansas stones and shaving your face with your park skis, but that's for another day.
Now, waxing. Get a big hunk of universal wax. In all conditions it will be much better than nothing, and will work very well in most conditions. Get ONE stiff nylon brush and a scraper. I started the arc of my home tuning work by crayoning on the wax and then rubbing it in. That's the cheapest way to do it, and it's impossible to harm the base that way. But if you've got a wax iron, great, just be careful about applying too much heat. Start by brushing the ski vigorously, wax, wait till the wax is hard, scrape, and if you're into it, brush again. If you don't brush, or for that matter even scrape, your skis will start out slower, but they'll speed up. All done*! Keep an eye on your bases and repeat waxing regularly. I try not to go more than 3-4 days max on snow without waxing, but mileage may vary.
*Note: if you want to spend hours of your life and your kids' college fund on waxing, good news, the sky's the limit! But the curve tracking return on investment rapidly bends to horizontal.
