I scan a lot of negative and slides (probably 10,000 sides and who knows how many negative frames), and I make inkjet prints from some of them. Your scanner must have a transparency unit. I use an older scanner, an Epson 4870. The V500 and V700 are both comparable and will more than do this kind of job. I use an Epson R2880 to print, but you could just as easily use a lab.
The most important things when scanning slides and negatives is for everything to be as clean as possible, and to scan at a high enough resolution for what you want to do. Just do the math. If everything is clean and scanned at high enough resolution you can make some very nice prints.
Inches x DPI = pixels
You want an image that's 11x14. To print it you need 300 DPI so you multiply. That tells you that you need an image that's 3300 x 4200 pixels. Now measure your slide (35mm is 24mm x 36mm or .944 x 1.417 inches) You have the pixels you need from the first calculation, and the inches form the size of the object you're scanning. Plug those into the formula (you only need to do the long side really)to get a DPI of 2964, go ahead and round it up to 3000. That's what you need to scan at.
Now Epson scanners (as well as some other brands) will do all of that math for you. Just tell it your output size and the DPI for that output size and it does the rest.