Firstly, do you calibrate your own monitor? If you don't, you can't really be sure if it's the prints or your monitor that is out of whack. But if you use a calibration device, you can be reasonably sure that what you see on your screen, is what you should get in a print.
Secondly, as for parts of the photos getting cut off...this is a common mistake/misunderstanding. You need to realize the aspect ratio of your images and the prints that you want. For example, look at a 4x6 print and now look at a 5x7 print and an 8x10 print....they each have a different ratio....so if you took a 4x6 image to get an 8x10 print made...something would have be cut off. Most of the kiosk machines that I've seen, will let you choose how the image gets cropped...but the default is probably right in the middle. As mentioned, the best thing to do, is crop the images yourself before you take/send them to get printed...that way you know what you are going to get.
There are plenty of places to get good quality prints...what city/area are you in? I usually recommend using a local lab so that you can have somewhere to go and someone to talk to, in case you need it. But there is nothing wrong with ordering prints on-line either.
I use Technicare, which has offices across Western Canada. I've used London Drugs with fairly good results. I used to use Blacks/Astral.