Spending any money on a logo is simply not necessary in your position. Until you feel like you need to cultivate a brand, don't do anything. When you do, consid

Spending any money on a logo is simply not necessary in your position. Until you feel like you need to cultivate a brand, don't do anything. When you do, consider just picking a unique (but not too unique) font for the app's name. You can pay for the font if you must. Designers get offended by this, but I've yet to see a case where logos are even slightly important to a bootstrapped business. You can always change it later.