I'd get a decent 30W soldering iron. One that has replaceable tips. You won't need more than a 30W iron for electronics.
Get a soldering iron stand. Preferably one with a sponge pad for cleaning the tip during use.
There's all kinds of solder out there. Go for lead free stuff that contains flux. That way the joints are cleaned as you solder.
And you can use either solder braid or the pump for de-soldering.
You can get an item called 'helping hands' that can be useful for holding boards and components in place while you concentrate on getting the perfect solder joint.
I find the most important part in soldering is getting the two items up to temperature. If one of the parts is too cold you'll get a dry joint or a solder with a matt finish.
Get your iron, wipe the tip on the damp sponge, apply a little solder to the tip, apply tip to the joint ensuring that the tip is in contact with both items, I.E. the circuit track and the component lead, little more solder to the tip. You'll find that soon as it turns molten you'll move the solder away from the joint slightly and just 'feed' the molten solder joint until done. Don't over do it. You want a shiny, perfect mountain shaped, joint.