Generally the method depends on whether you want to save the IC, the board or both.
In most cases, not yours the board is of utmost importance and the IC expendable, so the method seeks to minimize pcb damage, for that, for DIL IC's, I cut the IC pin with very fine needle nose pliers close to the IC body, remove each pin one by one and clear the pcb holes with the sucker, with minimal heat stress to the pcb and its pads and tracks.
Or, the sucker method one by one to save the IC and the pcb. But, there are various quality suckers and you have to be patient, adding fresh solder and making sure after the suck that the pcb hole is clear and when you push the IC pin sideways in the hole, it breaks free and every pin has to be perfectly free before you pull on the IC, or it can damage tracks and pads.
The other method that works very well, if done correctly is a tool like this on your soldering iron:
Again fresh solder is added first, all the solder on all pins is heated until you are confident it has liquified, then the IC is pulled from the board.
I use similar tools to remove surface mount IC's and the tool goes over the top of the IC and all the pins heated at once (after applying a lot of solder over the the pin arrays first) then the pcb is cleaned with wick and IPA .
Another trick to remove surface mount IC's , but on a pin by pin basis, is to thread some thin enameled copper wire in the gap under the pin and the IC body, down one row of pins and tie it somewhere nearby. Pull on the other end of the wire, keeping the wire low and parallel to the pcb surface, not pulling upwards on the wire, while heating a pin, the wire lifts the pin off the pcb track, but without putting any upward pulling forces on the track, in fact it pushes the track toward the pcb, preserving the fine tracks.
The problem with blowtorches, the heat can rise very quickly to uncontrolled and unknown levels, destroying the pcb and any parts you are trying to salvage, I would never use one.