My favorite cutter is gingher for the 45 (find it on ebay cheap) and olfa quick change for 60mm for thick stuff. I have the june tailor mat and I love mine but a lot of people hate that mat, but I have had mine forever so to each his own. If you buy the shapecut, buy the 12x18 because you can cut more strips than the 12x12.

I just purchased a True Cut 6x24 ruler & their big square ruler along with their angled cutter. I saw it used at a quilt shop and they let me try it. DH and I are both enjoying using them. Angled rotary cutter is easier on the wrist. My original Olfa mat is still holding up. I just don't trust the accuracy of the markings.

I forgot to say that your basic rulers may be something you need to see in person before you buy. My 6" X 24" Omnigrid is probably 20 years old. I have used it for sewing and quilting and used to love the markings to the 1/16ths. But now I have trouble seeing that arms length distance as clearly as I used to, even with new glasses. Those tiny yellow/black markings aren't so easy to see anymore. I found the June Tailor Shape Cutter Plus on sale at Amazon, and found that in addition to the slots, I liked the black ink. I may have to save up and use a coupon to buy a new utility 6" X 24" ruler with black printing.

Martelli cutters and mats
 

If you want the Cadillac of cutters and mats take a look at the Martelli ones.
Go to http://www.youtube.com/watch?v=tifHqHiGEy8. They are expensive but the company has frequent sales at Redline on their site. Joann's has the cutters and blades on sale now. Their website is Martelli Catalog: Cutting Mats.

I have had the Ergo cutter for about 6 years. It is one of the easiest to use tirelessly. You can cut many layers. It rolls like a rolling pin. The mats are self-healing and made out of heavy material. The rulers do not skid. The company is fantastic to deal with. When I had a problem, I mailed the cutter back to them and they replaced it.

I second the Martelli mats and rotary cutters. They are wonderful! Don't know how I managed without them especially since I was diagnosed with rheumatoid arthritis. Cutting is fun again. I've had them about 6 or 7 years now and they're still look like new.

welcome from virginia ...I use my green olfa mat most often.....45mm olfa rotary cutters...

I use a Fiskars mat here at home. Grey with yellow lines. And I have a Fiskars cutter, too.

But at the shop we have Olfa and use Olfa cutters as well. I like both brands and have no trouble switching back and forth.

I refuse to use anything other than Creative Grids rulers. They are the best...lines marked well, 1/8" increments, built-in grippers on the back, and very accurate.

I like the Olfa cutting mats and rotary cutters. I LOVE my 6 x 24 O'lipfa ruler (I think that is how it is spelled). It has a lip on it so it is easy to line up and make sure the ruler is square with the mat before you cut. As budget allows, it is nice to have cutters in different sizes - I use my 45mm most, but also use a 60mm and a 28mm often. If I could only buy one cutter, I would go with the 45mm.
Good luck and welcome to the world of quilting! You are going to love it!

I would buy an Olfa mat and on a ruler fund one that you are comfortable reading. I can no longer read the yellow ones so use only clear ones with big numbers. Welcome to the board.

I bought both of my mats at a Remote Control Model Shop(DH's hobby-one of many !!lol) a while ago and paid OODLES less than one at any fabric store.. so maybe that is a thought .. it has a few extra items for the RC'er in the family, but has a great grid system. One is grey and one is green, I use them both and are the same thing as the mats that Olfa makes (probably the same manufacturer just for a different type of hobbyist!)