The quick answer - not particularly, unless you plan on becoming a highly recognisable national or international brand.
For the vast majority of businesses, brand recognition isn't that important. Lots of people in marketing like to talk about brand, but unless you're MacDonalds or Coca Cola, your 'brand' should be about good customer service, great prices and delivering what you promise, not about a flash logo, corporate colours etc.
When it comes to your logo, it doesn't need to be fancy, it just needs to look professional, and by professional, I just mean that it should look like you didn't get it drawn by a five year old!
The most important things to bear in mind when designing a logo, or if you are going to get one designed are:
You can get a professional designer to produce one for you, but you shouldn't be paying more than about £200 at the very, very most. Alternatively, there are a wealth of online logo design services that are all automated, cost significantly less, and for the most part produce pretty good results.
As an example, I tried www.looka.com with a 'company' called Genius Plumbing, and the results, although not mind blowing, are more than suitable. It took less than two minutes and for one of these it'll only cost you £50.


