Nobody said Hood? WTF
Should be first on any list of training mountains fer noobs.
In late spring/early summer, maybe, but in winter, Idon't know if I would agree (at least not if you were planning on the summit). If you are with an experienced partner, then yes.
========================================================================================================================================
Anyway, as mentioned, (to the original poster) your criteria is vague and open and many places could fit the bill.
Personally, I'd start somewhere like the Sawatch Range of Colorado, the La Sal Mountains of Utah, or the Snake Range of Nevada (for example; these are all random choices out of dozens of possibilities) before moving to ranges such as the Cascades (unless you have experienced partners willing to show you the ropes per se).
Also, keep in mind that all that gear you list isn't going to protect you from something like an avalanche (or crevasse). Those kinds of things take experience.
A possibility would be to join a group where inexperienced climbers are allowed on trips. For example, 14ers.com is having a winter gathering soon. Sometimes summitpost does as well. So do other places in the country. Another possibility would be to take a climbing course (many of these are available, especially in places like California or the Cascades).
If you do decided to choose an area close to where I am, I could climb something with you, but I just burned all my vacation time in Nepal, and have another trip to the Cascades in July and out of the country later this year, so it would have to be confined to a 3-day trip.
PS, are you planning on going solo, with a friend, group, etc.? With someone experienced? It would change the answer concerning what mountains to climb.