I agree with TLS - business and friends don't mix. (You guys may be the rare exception, though). Also complicates the accounting. Might be better for one of you to employ the other. Or just each go into business for yourselves and you can work with each other when you need help. Just make sure you have a good understanding with each other of how things work.
Most guys would say you need a trailer. I don't use one and you can do without it, but probably you should get one.
The first rule of equipment is ALWAYS buy commercial quality.
Most here would probably advise get a big mower. Probably you can do what you need with 21" mowers. I use Honda HRC215's, which are about $800. The more powerful 216's are over $1000. There are different features available with these mowers - I use the ones with BBC (blade brake clutch) and self-propelled. (HRC215SXA, I think). Toros are good too. Tons of discussions here on lawnsite about which 21" mowers are the best.
I don't use edgers, I edge with string trimmers (weedeaters).
Currently using Honda HHT25S trimmer - about $300. Lots of discussion here about trimmers too and also about trimmers vs. edgers.
Lots of guys use super-powerful backpack blowers but you can get adequate blowers for $250 or so.
You might want to get a chainsaw - I like the Echo CS300 - about $200.
And you will want to get a bunch of smaller tools - loppers, shears, pruners, shovels, rakes, etc. A.M Leonard is a good source for quality tools - http://www.amleo.com
Maybe some good ladders - I use 6'and 10' fiberglass stepladders - for tree trimming, gutter cleaning, trimming larger shrubs, etc.
You need to find out what to do with yard waste. In my city we get to take it to the compost facility at no charge. Some LCOs actually buy land to dump stuff on.
Keep all your receipts, record all your transactions and try to find an accountant you like.
And get all the books you can, and keep reading lawnsite!