If you know that you are not going to start with a compressor and will be filling at a dive or paintball shop, I'd suggest the first thing you do is find the shop that you intend to fill at and find out what they need for you to do it. That will let you figure out what is best to buy - some can only fill to certain fittings, for example some dive shops can't directly fill a firehouse (CGA347) fitting and may not have an adapter. Such an adapter is available, but is an added cost if you were not planning on it. Two other important things to find out (in addition to whether or not they will fill and cost) is the fill level you will get from them (some only fill to 3500-3600 psi, as that is where a lot of SCUBA use stops) and how long it takes to fill (some want a drop off and fill for a later pickup, leading to two trips to the shop for every fill). In my case, the best shop for me could give a me a full fill for a fair price while I waited if the owner was there, but needed me to leave it if he was not there. Know what you are going to be dealing with before you make a final decision.
For the cheapest entry into tank ownership, you could look for a used SCBA tank that is still "good" in it's 15 year life and also still covered under a current hydro test. I did that when I started, and bought used 45 minute tank that was ten years old but had a fresh hydro, giving me five years of use at my local dive shop before I had to do anything different. In the end, the "cost per year" would be about the same as new, but since you are buying only 5 years (or maybe less) of life the total cost up front is lower. Your fill station costs (if separate) are good for much longer.
In that time of certified use, you may find that you are fully addicted to airgunning - and if so you have the option of replacing your out of date tank or going the compressor route. But the option is yours, and was made available with the lowest cost up front. After my five year usage at the dive shop was up on my used tank, I bought a compressor instead of a new tank (the good old Shoebox, back in the day) and kept filling the tank I had. Eventually I added more tanks to the mix as I am fully in this hobby (one was a DOT "Guppy" from Joe B and the other a 9L CE Acecare tank). I find filling from a tank to be the bast way to fill, so I am glad to have multiple tanks and the compressor to fill them.
Welcome to the world of tanks!