Soldering IC directly to stripboard
For the IC holder (called an IC socket normally) the most difficult part will be desoldering it without some some form of solder sucker. Personally I'd cut away the plastic section with side-cutters and then remove the pins one by one considering you don't want the socket. Then either user a small hand-held solder sucker (they only cost a few dollars) or if you don't have one maybe push through a piece of wire while applying heat to clear the hole of remaining solder.

For soldering the IC directly it's easy to be paranoid but DIP packages are often wave soldered which involves dipping in solder and making every connection at once and the pins themselves will dissipate a lot of heat before reaching the die of the chip. Just to be a bit extra cautious as you improve your soldering technique maybe just wait 15 seconds or so between each pin to give it a while to cool down. You should find the top of the chip will barely become warm, it if is just wait a while until it cools down.

I suspect the trickiest thing is likely to be removing the socket without tearing off the tracks on the stripboard. That's why destroying the socket and removing pin by pin is probably easiest.