New to ice as in no experience, or some experience?
If little to no experience, then start with a TMC. And you can't go wrong with Alpine Guides or Adventure Consultants (but there are others) -- they have a lot of useful information on their websites. Unlikely that you'd see steep ice on a TMC, but it is essential to get the core skills first. This is also the more cost effective way of getting experience -- unless you have a patient and well experienced friend who is willing to take you out and teach you.
If you have some experience then you could look to do a guided ascent or (advanced) private instruction -- again look at the websites of the guiding companies for costs / possibilities. This will give you the most freedom to get on better lines, but it will be expected that you have the core skills and fitness. It will also cost more.
And January is probably not the best month for steep ice. You may want to think about going earlier in the season -- especially if you need to first do a TMC. If you are new to the mountains then be prepared to take it slow, which often means saving some of the bigger routes for the next season.