63/37 is recommended because this mix of metals in the solder makes it "euctetic" - this means that the solder changes from liquid to solid within a very narrow temperature range, around 1 degree Celsius.
So when you solder, as soon as the solder goes below 183 degrees Celsius, it practically "snaps", it goes from liquid to solid. It's nice because you can literally see the change with your eyes and you know once it's solid, your job is done.
The more common 60/40 solder is not euctetic, it will go from liquid to solid across a wider temperature range, at around 180 degrees celsius. This makes it a tiny bit better for hobbyists with poor quality soldering irons, as the solder will stay liquid for longer time but once you use 63/37 you'll appreciate that euctetic property.
63/36/2 is also euctetic and the 2% of silver can be good if you're soldering a lot of ceramic components like surface mounted resistors and capacitors, but fewer and fewer components actually have silver on their terminations, to make sense to use solder with silver for better chemical connection between solder and terminals. I'd say it's not worth spending the extra money if you're a beginner.
I can't stress enough how much it matters to buy a solder from a company with reputation like Multicore, Kester, Henkel , Stannol , Edsys, MG Chemicals
You should get solder around 0.5mm - 0.8 mm and for a beginner, 2% or more flux would probably be best choice.
Fluxes ... you have RA (activated rosin) , RMA (rosin mildly activated), no-clean ... stay away from others like organic or water soluble fluxes, these often require cleaning.
RA, RMA and no-clean you can usually leave the flux residue on boards and they won't cause problems, and you can clean them with isopropyl alcohol or aceton or other solvents.
Since you're in Israel , see if you can order stuff from Farnell.
Here's the solder wires they have :
https://uk.farnell.com/c/tools-production-supplies/soldering-stations-accessories/solder/solder-wireAnd they also have some soldering stations which may be cheap enough to be worth buying from them instead of waiting for packages to come from China, here's a link
Soldering stations :
https://uk.farnell.com/w/c/tools-production-supplies/soldering-stations-accessories/soldering-stations/soldering-stations/prl/results?sort=P_PRICEFor example they have the classic Hakko 936 clone, rebranded Yihua (or whoever makes them), tips are cheap, heating elements are cheap etc etc :
https://uk.farnell.com/tenma/ss-207bc-f/soldering-station-60w-240vac/dp/2565326They also have the rebranded Atten AT938D stations which are decent :
https://uk.farnell.com/tenma/21-10115-eu/soldering-station-60w-220v-eu/dp/2062627I also wanted to recommend TME.eu , they'd probably have cheap shipping to you, but they seem to stock only lead free solders these days and the soldering stations they stock are not cheap.. the cheapest i would be comfortable suggesting would be around 120$ there.