Rooguchi is an excellent choice to start with - a strong growing, free-flowering and robust plant. It typically does have a long bloom season but that does depend on where you may be located and the siting of the plant itself but 3-4 months is perfectly reasonable and could be in bloom even longer. Rooguchi is considered an herbaceous clematis, meaning it dies back to ground level each winter. Therefore, it should be cut back each season, just as one would cut back the old foliage of any other flowering herbaceous perennial. These types of clematis tend not to vine or climb well anyway, so cutting back annually keeps things tidy. As to how you can extend the bloom season, my suggestion would be to make sure the plant gets adequate sun and has the soil, water and nutrient requirements it needs. The clematis that will grow well with the least amount of effort and problems will tend to be species clematis or those very closely hybridized from species clematis, like Rooguchi. These tend to be immune from issues like wilt and and in many cases, powdery mildew. These all tend to be included in pruining groups 1 and 3 and excludes the vast majority of what are considered the large flowering hybrids or pruning group 2 clematis. Unfortunately, your selected vendor is offering ONLY group 2 selections, so none of these would be ones I'd recommend. Typically the vitacellas and vitacella hybrids tend to be the varieties most often recommended for novice growers. These would inlcude cultivars like 'Polish Spirit', 'Etoile Violette', 'Betty Corning', 'Huldine', 'Minuet', and a host of others. Vigorous, hardy, disease-free and long blooming, any of these would be a good choice.

The Jackmanii benefits from a hard prune annually, so just whack it off to the second or third set of buds per stem and she will fill in fuller than previously. The Duchess, since she is type 2, can be trimmed back the same way, though you will lose the first flush of flowers for this year. However, it will still bloom, just later than usual since it is only on the new growth. Since I live in an area where often my type 2 get killed to ground level or at least the snow line, I always expect to just have one set of blooms. So I can testify that the D of E will be fine if you hard prune her this year. If you can keep a few longer vines that are in better shape you may get some early bloom as well as the later bloom.

It looks to me like you have two different clematis there. Perhaps they both came in the same pot initially by accident, or perhaps the larger, lighter colored one is a seedling. The darker on on the lower right that is "funny looking" looks to be 'Multiblue' and since the other clematis is blooming at the same time, both are probably type two prune clematis. Generally, folks who feed their clematis use rose food which is formulated for good bloom, so you might try that. Also be sure that the clematis gets regular soaking to reach deep roots when the soil is dry below the surface, and adding a mulch to help maintain even moisture levels. I like the current clematis that you have. If you want a really dark purple as well, you can add one or more that blooms later in the season (type 3 prune, which means cut down to a few buds annually since they bloom on new wood and this keeps the flowers lower) on another trellis. Viola, Mikelite, Etoile Violette, Romantika, and Jackmanii all have rich purple flowers and are type 3 prune. I've seen all of these in the last year or two on the lists of one of the mail order nurseries I use: Brushwood, Silver Star Vinery, Hummingbird Farm, and Joy Creek. Viola (with Betty Corning, the lavender bell) is in reality a bit bluer in color Mikelite is a bit less pink than this, but still has more red/pink than Viola Romantika

Not sure of your source but clematis do NOT stop growing without a trellis or other support system - they either create their own (sprawling up though other plants or any other vertical structure) or they act as low spreading groundcovers. But if you want vertical growth, providing some sort of climbing support is advised. Fishing line is a great idea - it is virtually invisible - but make sure whatever you use to attach the fishing line allows some distance/air space between the wall and the vine. This will allow for proper air circulation (reducing disease issues) and keep any wet foliage away from the side of the house.