As with most mountaineering equipment, there is not one magical item that works for every eventuality. When investing in boots, you need to decide when, and for what, you are going to be using them the most. There will have to be some compromise somewhere along the line. The additional cost of buying multiple pairs boots to meet the demands of the mountaineering calendar will keep you more comfortable in the long run, and your boots will last longer (long approaches or rock scrambling in your expensive high altitude boots will considerably shorten their lifespan).
For winter and spring objectives a full shank, fully rigid boot is the norm. Nowadays, advancements in construction and materials means that plastic boots are out, and leather or synthetic boots are in. The Go-To boot here is La Sportiva Nepal Evo or similar. If you anticipate doing more cold weather or high altitude climbing, a synthetic double boot will be warmer and easier to keep dry. Gaitered models are becoming more popular but often still need an additional standard gaiter in winter to deal with deep snow on approaches and they can be difficult to dry out during prolonged stays in the mountains.
Use these boots for winter ice and mixed climbing, Aoraki/Mount Cook and Mt Aspiring via the Ramp.
If your aspirations are less vertical or only short steeper sections, then a 3/4 shank boot like the La Sportiva Karakorum Evo or similar will do the job. These will also be more comfortable on walk-ins and be more useful later in the summer season when you are likely to be scrambling more rock.
Use these boots for glacier trekking, Mt Earnslaw and Mt Brewster
Once you hit high summer and beyond, and your objectives transition from the snowy glaciers to rock, then a lightweight and comfortable summer boot like the La Sportiva Trango Evo or similar will be perfect. The good news here is that these types of boots are significantly cheaper than mountaineering models.
Use these boots for the Remarkables Grand Traverse, Mitre Peak and McPherson-Talbot Traverse.
All of the boots mentioned above will have crampon compatibility. The only big thing is that winter enthusiasts will opt for a dedicated ice climbing crampon (Grivel G14 or Petzl Lynx). For all other objectives, a general horizontal front point, 12 point, general mountaineering crampon will do.
For attachments, fully automatic (front and back bail) crampons should only be used with fully rigid boots otherwise a semi-automatic (universal toe and automatic clip at back) will be the go-to. Some crampon manufacturers now have systems that allow you to switch the attachment method depending on what boots are being used.