The best snow for skiing is usually Feb - early Mar, IMO. You have less issues with the snow getting slushy in the afternoons as you do in late Mar, early April.
Much better chance of Colorado's famous "champagne power" as well -- dry, fluffy powder which is the absolute best snow to ski on. Later spring snows can be big, but often they are a wetter snow and not as good as the dry snows.
After end of Feb, the crowds really increase. Unless you are skiing in the back bowls or other more advanced areas, you will be spending more time waiting in lift lines. But the weather is nicer, so it is a tradeoff.
Simply put, there is no "best ski week", just a lot of choices.
Edited: I also want to add, if you are staying a week in Breckenridge, definitely check out some of the other great ski resorts in the area as well. You can drive to Keystone or Copper Mountain within 20-30 min from Breck. Keystone is usually included w/ your Breckenridge lift ticket, and has some fun night skiing (If you haven't tried it, you just have to experience it at least once). Arapahoe Basin is good for a bit more advanced skiiers and Vail (45 min) is definitely worth the drive for a day of skiing there.
This makes me feel a little bit lucky. Somewhat blindly I bought a Week 9 for skiing Keystone and Breckenridge for my Son primarily because it was available the year he needed a place to stay and it was cheaper than renting. He and/or his Marine buddies have used it almost every year since.
My experience in renting ski weeks is the best demand is during a mid March spring break week. Many people get one day off during President's week but a lot of families will spend a full week at a ski resort during spring break and I've found that you have a better chance renting full weeks during spring break.
Best ski week for me is President's Week - timeshare week 7 - as all our kids have the week off school and many families use it for a family ski holiday. Next best week is any in February or March as the snow is most usually reliable.
Unfortunately, then these non-holiday weeks equate to "me" time and must be compensated with extra family holiday time.