First off I'm going to start with saying stay away from Kalkwasser ATO dosing!! It's easy and not much fuss but it is wildly inaccurate and really uncontrollable. It's useful for some tanks but for you and anyone running a serious sps tank I would avoid it at all costs due to the inability to really control it and therefore the fluctuations that it causes.
Now that I have that out of the way onto a more serious note haha.
I suppose I'll continue on my Kalkwasser explanations while I'm on the subject. Kalk reactors aren't too bad when it comes to keeping up certain elements as they effect not only Ca and Alk but they'll also keep your pH nice and high too (saturated kalk has a pH of about 12!). The reactors work by running a saturated mix of water of kalkwasser (calcium oxide or calcium hydroxide depending on brand/type), some use the pure saturated kalk water and others leave the undissolved powder in the reactor and mix it and then dose an almost super-saturated milky kalk substance. Most of the time kalk is dripped very slowly into the tank so not to throw anything off with it's high concentrations. Meaning a slow and constant feed on Ca, Alk and pH to the tank so it's really necessary to really tune in the flow rate as quickly as possible.
The downfalls of kalk are that (as I'm sure you know) calcium oxide and calcium hydroxide are not human friendly substances!!
Protective Equipment needs to be worn, the powder is harmful if inhaled, ingested or it comes into contact with you as it is a
caustic substance. I may be being a little over warning here but it is a dangerous subject and the science buff in me says there's no such thing so please do be careful if anyone is thinking about Kalkwasser!
Personally for you and most people I wouldn't worry about kalk, with the quality of balling products and part-dosing. Kalk is a little tricky and while it's good once set it's still not as easy or as straight forward as other methods
Calcium reactors are big, expensive and attention intensive pieces of equipment and systems but they are awesome!! I would love to run CaRX!! So good and really high quality dosing source but they can be quite dangerous and catastrophic if you're not always paying attention to them. They use CO2 to dissolve a calcium media and then flow it into the tank that way. So you need a pump, CO2 bottle, some monitors, the actual reactor and then the various intermediate parts. It is a really solid source for your tank and especially when you have high consumption rates in your tank. Only problem is they're recommended for higher consumption tanks but you can buy smaller units, they are a lot of work but well and truly worth it in my opinion and would be my weapon of choice if the stars align!!
I'm going to group balling methods and part-dosing together as they are the same things just balling is an expansion of part-dosing. They both involve deciding on elements as aspects you want to be maintained and dosed and then it's a matter of fine tuning amounts of what you want to directly dose. This is what I would recommend for you or anyone that is beginning to dose as it can be the most straight forward and the easiest to control and adjust! This is pretty much as straight forward as you get, especially if you're buying a dosing unit too (kamoer's are solid brands and cheap too, GHL if you can afford it). These methods of dosing involve creating your concentrated dosing liquid and according to your consumptions starting out with small amounts being dosed and slowly bring it up till there's no real variance between each water change.
This method is also the most expandable as you can go from two part (Ca and Alk) all the way to balling which is everything, all elements and salt! (Check out GlennF's thread for info on proper balling of everything and his methods!) Three part is the most appropriate as Ca, Alk and Mg need to be in balance and once you have your liquids and containers set, you decide your amounts and set it on the doser, testing and monitoring and adjusting is required till you find the right balances
For you though I would highly recommend getting a dosing pump (I use a kamoer 3-channel) and some three part (I use Fauna Marin Balling light powder and mix it myself and it's amazing, super high quality and accurate
Ca, Alk and Mg, I'm not using the trace elements though(yet)), you can also get some potassium but I would hand dose that till you know how much is needed then set it up. Have a look at calcium reactors if you'd like but I'd definitely recommend dosing pumps and dosing liquids
Vodka and sugar are used to feed bacterial populations (as carbon sources) and things like that, not for elements for your corals. I can go into that if you'd like though