as much as you have.
you have to realize some people have access to a lot more money to start with than others. this doesn't mean that either one will succeed, it just means they have more options.
That's all money will give you, is better options.
How much determination you have is more important in my opinion. Don't get me wrong, you do need money, but if you only have $500, you can make it work. Slowly building up. If you have $10,000, you'll have a better line of equipment starting off, but will also have to pay for it all by doing good work.
I'd say a reasonable starting amount, depending on if you are starting part time or full time would include:
Truck, mower, trimmer, blower, edger
so whatever you can get by spending to get started with those is about your main concern.
Also, try to get a few bucks saved for advertising, if anything for handing out flyers, to start up some work.
As a reference, I am mainly writing this response the way I have, because I started with just about nothing. Finally this year got a Truck, which is a HUGE help, so if you have one, or can save for one, I'd consider that essential at some point.
Good luck with the business, sorry to go so far off track, but your question is too vague to give a $ value. You'll need to state how large the lawns are you'll be doing, and how many, etc. to really price out the right equipment.
But since you asked, I'd say bare starting out, as I did
now this is not commercial grade stuff, but you need to start somewhere, so this may last you a season to generate some income, and start to get your name out there.
Hope this helps some
TWINS Lawn Care
Give your lawn that first impression people will look twice at!