For electronic soldering around the studio, you need a fairly small iron. 25 watts is just fine, and actually even a little bit large for most patchbay/instrument/cable work. 35 watts might be necessary if you anticipate doing a lot of heavy soldering (like copper tape for shilding guitar pickup cavities, where the copper will sink too much heat away from the joint area with a smaller iron). You'll almost *never* need more than 25 watts: too big an iron will get you into more trouble than you want, as the extra heat will get to places you don't want it to go to.
Tips: long, skinny, slender, conical. You won't need many: I've been using the same long conical tip on my Weller iron for 3 years. With care and cleaning, they're pretty long-lived. The tip will slowly erode, as any copper in it goes into solution in the solder- but that's thousands of joints down the road... Keep a poist sponge at hand for cleaning the tip prior to each joint.
Home Depot? Doubt it, but it is possible. Most of their soldering gear is intended for plumbers: million-watt guns and nasty, disgusting acid-core solder, either of which will disintegrate a printed ciruit board at first glance. Not applicable to our needs. But look anyway- I don't know what they have. Worse comes to worst, order online. Home Depot won't have decent solder anyway. Rat Shack probably won't either.
Solder: Kester 44, 60/40 rosin-core solder for general purpose use. Or, if you really want to do it right, Kester 62: 62/36/2 silver solder. That is twice as expensive, but is *righteous* stuff for audio work. Thanks for reminding me- I'm almost out, and need to order another pound. Whichever type of solder you get, the 0.025" dia stuff is easiest to work with.
Cabling: yes, cable is good. There are a million options: Belden, Canare, Mogami, Gepco... You'll need to get catalogs from
http://www.markertek.com ,
http://www.fullcompass.com ,
http://www.mouser.com . Those folks have wire, connectors (I like Neutrik), solder, and irons...
Wallplates: Markertek, or build your own.
Practice your soldering/desoldering technique on junk gear or scraps of 24AWG wire before attacking anything you want to keep. Just remember: you apply the heat to the parts you want to solder, and then let the solder melt onto the hot parts. Heating the solder and dripping it onto cold wire will give you a cold joint and a mountain of headaches. The wire has to be hot enough for the solder to melt on it, wick onto its surface, and get a good bond. Practice!