Similar to what others have said.
Its easier to come up with a plan knowing what amount of capital your starting with but some basics in my opinion would be:
decent walk behind mower you can pick up one here all day for $500-800.
I would skip the 21".
Get almost any trimmer. New is better will save headaches but you don't need top of the line anything. It will only be working 1-2 days a week I am guessing.
There are some decent handheld blowers but I would really try for a backpack.
various hand tools shovels, rakes, pitchfork ect.
As for work hustle for anything. When starting out you don't have alot of choices to say no. It's important to do as much as you can. Do it well and get your name out there.
Alot of people say get shirts I disagree with them being priority but if you have some extra cash the do help build a brand and help give you pride in your company. If not buy a 5 pack of a color t shirt and use those. It will have the same effect in terms of building a brand.
Advertising: Like others have said get out do flyers they are cheap.
get involved in the community in some way.
Ask friends and relative for work. Its a great starting point.
Join a BNI group or refferal group if you can.
Then spend your spare time with all of the free advertising out there. Facebook,myspace twitter, craigslist, google, yelp, Lots of cheap ways to get websites and so on.
Most important reinvest your money into the business. Don't take more out than you need and remember the difference between wants and needs.