Referrals from your clients is hands the best way to get new clients. Also if you can get in good with a supply distributor they may be willing to give out your company name if you do good work. I don't know diverse you are as far as lawn mowing, landscaping, weeding, mulching, hardscaping, etc..
I would definitely go door-to-door in the neighborhoods you are already cutting lawns in but don't waste your time going to other neighborhoods yet.
Also unless you are buying out another small company I wouldn't plan on getting 30 new accounts, you can aim for that but it will be hard to get 10-15 new lawns.
I would also advise that you upgrade your weedwacker and possibly your blower to a backpack model. I personally love my Echo equipment and don't plan on even trying other brands such as Stihl and others.