Don't know about price wise, as masons are often members of a Union and charge a fixed hourly labor rate, but quality wise, you would probably be wiser to pay more for a job that will last as long as the dwelling!
Check with friends and neighbors for references or as a last resort, drive around your neighborhood or others in the surrounding area to find a walkway like you want and knock on their door. You could begin by saying, "I was driving by and saw your very attractive walkway and want one exactly like it!" and ask for the contractor's name.
Be sure to ask for their evaluation of his/her performance and their satisfaction with the work/value received.
Be sure to ask for several references from any contractor and CHECK THEM OUT!

When they remove the existing concrete walkway, you might have them cut it with a saw into small squares or rectangles and recycle it into a dry stack border or low walls for your raised beds. (Saw that used at the Anchorage Botanical Garden on a recent TV garden show.)
Good luck!
Rb

The best contractor for this project is you yourself! Seriously, laying a new paver or flagstone walkway is a very doable DIY project and you will save a ton of $$ by doing it yourself.

The hardest part of the project will be removing the old concrete path. But although that will take some serious elbow grease to accomplish, it can be done relatively easily by you and maybe a couple of good friends (promise liquid refreshments when the job is complete :-)) My brother and I helped a friend of mine break up and remove a 30' long, 60 y.o. concrete driveway a few years back and I'm a grandmother! She wanted the drive gone for extra planting areas and I needed the recycled concrete for a design project I was working on. It took a couple of weekends, a strong pry bar and a sledge, but we recovered 3, 3/4 ton pick-up loads of concrete chunks and my friend doubled her planting space in her rather tiny urban garden. If you need to, rent a masonry saw to cut the concrete away from any steps. You can also use the saw to cut the old concrete path into manageable sizes but I prefer the look of naturally broken concrete chunks for recycling purposes.......you'd be surprised how many uses you will find for them!

As to designing and laying a new pathway, that is pretty simple. There are all manner of home landscaping books that outline the process, you can find instructions online or most stone suppliers will provide instructions as well. The most important thing is preparing a proper, level, compacted base. You can choose naturally shaped flagstones and fit them together like a jigsaw puzzle or select cut stones for a more formal look. The cut stones also allow for closer placement - naturally shaped flags allow for interplanting with grass or groundcovers if that is a look you prefer. Or, if your climate requires it, you can mortar in between the joints and remove the potential for any movement or weeds growing in the joints.

And remember to be generous with your sizing. Most builder pathways are uncomfortably narrow. A primary entry access should be no less than 5' wide to allow two people to walk side by side easily - 6' is even better. This will provide a wide, welcoming entry to your home and garden and the hardscaping is an attractive accent to planting beds or lawns. And I'd recommend using rigid edging to contain the pathway. This is typically sold at the same places one would obtain the stone and is easily installed when the base material is constructed.

The December/January issue of Fine Gardening has a great example of a new front entry garden with a stunning limestone paver walkway you could peruse for inspiration. Or just let your natural creativity flow!

Here is a link that might be useful: only one of many online instructions.........

No way no how will we do it ourselves. I just don't have the time, I don't want the aggravation, I want it done in one or two days - I'd rather pay someone to have it done right the first time with no headache to me. I am just not the DIY type for these types of projects.

I do appreciate the suggestion, though, and appreciate the comment about the wider walkway - I never thought of that, I'll definitely discuss that with the contractor.