Your soldering "station" looks very similar to this part, and from the name of the tips the 4 from reichelt should fit.
https://www.pollin.de/p/loet-starterset-daytools-ls-99kit-501746pollin delivers the same, several cents cheaper.
https://www.pollin.de/p/ersatz-loetspitzen-set-840176But 2 from the 4 parts are so useless, like the first tip is. Those pencilshaped Tips are only useful for very little pieces
with tiny heat-requirement. For more heat you need a tip in the form of a chisel or flat-screwdriver, the Horseshoe shaped tip
is as well an universal tip, If you hold your handpiece nearly vertical, you can use it for small parts, if you hold it in 45° you can heat
bigger parts fast. OK within the power of the heat element.
For the SMD-Kits, if you want to solder resistors, capacitors, or similar 2pin parts the pencil shaped tip is ok, but a small chisel shaped tip is better, because you can place a small amount of solder on the tip, that flows to your part, without separate solder. But you need
additional flux, put flux onto the pads, place your part above and touch it with your solder tip.
You can do the same with the 2 or 4 sided ICs. First Solder 2 pins on the opposite side of the part. After that change the soldertip to the horseshoe shaped and drag it along the pins, the solder should flow between the pad and the pins of the IC without bridges. If you have bridges, than you need solder wick. And if you can buy it somewhere, buy a roll with 100gr or more 60/40, 63/37 SN/Pb solder from good manufacturers. For SMD maybe 0,5mm is good for all other parts 1mm should do it as well. Leadfree is good for the big firms, where people must soldering PCBs 5 days and 8 hours a week. But for all of us, who need to solder less then 10 minutes a week, its a pita.