As to your question on cassette choice. SRAM makes a 12x26 9-speed while Shimano makes both 12x25 and 12x27 so you have three choices.
Sydney is correct about the dropout spacing. In all probability yours is already 130 mm since the same frame probably came with 8 or 9-speed components at a higher price. My son's 1996 Trek came with 7-speed RSX but is spaced 130 mm and my 1992 Trek came with Shimano 105 7-speed and is spaced 128 mm.
You could replace the 7-speed freehub body on your current wheel with an 8/9/10-speed body if the hub, rim and spokes are in good condition. Otherwise a new rear wheel is probably a better alternative.
Your current chainwhip will work. You don't need anything special to remove the old chain and any good chaintool (Park's CT3 is my favorite) will install a new one. BTW, be sure to use a new chain if you replace the cassette. If you go for 9-speed you will require a 9-speed chain.