I like what MOturkey suggested, "buying out" your partner's half. It should be much more economical for you to do that, rather than have to shell out a bunch more money at the beginning of next season. Figure out what your partner's half/share in the business is and pay him that amount.
Like stated previously, everyone wants to start at the top and have all the great equipment. I've been in this industry commercially for a few years and I am still not near the top. I'd love to have 8.5x20 enclosed trailers, new duramax trucks, and a ton of equipment....but those things all take time. Start out small and upgrade/replace as you get more work or as things wear out. I know you don't feel all that "professional" when using residential grade mowers or having to cover your equipment with tarps overnight, but we all had to start somewhere. Like I said, just give it time and build up your business as you gain it.
Your young and in school, DO NOT get into payment plans. Save your money, pay with cash.
'07 Chevy 2500HD
2010 John Deere Z925A 54" MOD
2011 John Deere Quik Trak 647A
John Deere walkbehind