if you are going to be soldering stuff then you need a solder sucker.
no matter how good you get at this you are always going to make the occasional mistake. that's when you'll need to suck up solder.
ignore solder braid for now. it's usefull when you start soldering things with tiny, close together pins but you don't want it now.
as for the solder sucker you have picked out, great idea in theory but i wouldn't use it.
while it would be good if you are taking something with lots of components appart completely, usually you just want to suck solder off one pin.
you don't want to have to heat that thing up for one 30 second job.
i have the kind you describe with the spring. like a mini bike pump but it sucks instead of blows.
yes, it's fiddly. yes, your solder hardens before you suck 50% of the time but it's still the best solution i have found.