What's your budget?
To blur the background, there are several things you can do. The easiest (or cheapest) would be to have your subject stand far away from the background while you are fairly close to them. Then, it great helps if you shoot with a large aperture...here is where a prime lens (non zoom) with an aperture of F1.8 (or bigger, like F1.4) will be helpful. This effect can also be enhanced/created with a longer lens...so 100mm, 200mm, 300mm etc....the longer you go, the more shallow you can get your DOF (depth of field).
The 50mm F1.8 gets a lot of recommendations because it's very cheap. Less than $100. It's also quite good in terms of image quality. Unfortunately, it's also very cheaply made...with lots of plastic rather than metal. If you can afford it, you might consider the 50mm F1.4...but it's three to four times more expensive. The 85mm F1.8 is also a good lens for portraits, if you have the space to shoot. Even the 50mm might be a little too long in some situations. You might consider a shorter lens...although shooting people with something shorter than 50mm might not be a good idea as it can tend to distort their features.
There are plenty of options...you might consider a zoom lens, which might be more convenient as an all around lens. You can still blur the background with a zoom lens, but you may be limited by the maximum aperture (usually F2.8 is the best you will find on a zoom...and F2.8 zooms are not cheap.
The options are many and varied. So what's your budget?
By the way, Welcome to the forum.