That will do the job. Check that it has a selection of different-sized bits.
Any Antex one with a small bit. Use good quality solder and if its new to you, get some wire and practice by soldering a grid or mesh and making a 10 x10 grid. Ie 100 solder joints. You're aiming for no sharp peaks. Practice makes perfect.
Tinkering with car electrics, as I often do, I've found a cheapo Halfords butane heated one to be ideal. It's small, it works fine for reasonably fiddly stuff, interchangeable tips available, and you take the tips off to use it as a mini blowtorch for charring the demerara sugar dusting on your macchiato.
Temperature control is important, especially on leadfree solders, get some wick as well. Without experience, using cheapo irons may mean knackering the components or pcb, bit of practice first will pay dividends!.
Some form of basic temp control is needed. You don't need a fine tip to do fine-pitch work; I used to do tqfp 144s with a fat tip at work. A bit of technique and lots of liquid flux can go a long way. If you can get lead solder, do. Its a lot less hassle.
