What soldering kit for tiny electronics?
Are you using SMD parts because you need to keep the the size of a board to a minimum?  If not, there are often through-hole parts that provide the same functionality. Obviously in you case, the resistors and LEDs, but there might be other ICs as well.  You don't have to use SMD parts for everything just because you have to for a couple, for example one or two ICs that you can't get in a through-hole package at all.

That said, a good soldering station for SMD work that is a fraction of the cost of most others is the Hakko FX888D.  You can get one from SparkFun for $100.  I worked for a company that got these for all the engineers because they didn't want to spend four times as much on a Weller.



You will probably want to buy some extra tips in different sizes.  I suggest getting a T18-I-T18; it has an extremely fine tip (0.2mm).



The next step up for working with SMD parts is a stereo microscope; the minimum for a decent one used to be around $700 but they are now appearing at half that price.  The important thing is to get one with a boom, like the one below, so it can swing out over your PCB. If you are going to be doing a lot of SMD work in the future, and can justify the cost, you won't believe how much easier it is to work with.