Carbon fibre is also interesting for photographers doing work in very cold climate. Aluminium, being a metal, easily reaches ambient temperature. When you work at low temperature such as below 0° an aluminium tripod becomes uncomfortable to work with, you have to use gloves and at very cold temperatures your hand may become "glued" to the cold metal. It also tends to grip more easily.
Carbon fibre is less elastic than aluminium. I'm not sure it would "handle" vibrations better.
If you need to use your tripod also on grass, sand, earth, look for tripod legs with the possibility to mount "spikes". The more comfortable ones are those which have retractable rubber feet so that you can have rubber, or spike on the ground without carrying accessories with you.
Gitzo tripods normally have a very intelligent accessory, a hook on the lower part of the central column. You can hang something relatively heavy (such as your photographic bag) to the hook so that the entire system becomes heavier and so less prone to vibration. I suppose with a bit of DIY the same solution can be applied to most any tripod leg. This somehow makes a lightweight tripod "work" as a heavier tripod, without paying a price in terms of weight as you have to carry your bag in any case.
Considering that portability is not extremely important for you I wouldn't make without a central column. A central column is practical but only if you raise a few cm (let's say 10 - 15). Don't use the central column to extend the camera position much above the legs unless the camera you are using is very light and the lens very wide angle. I use it for small adjustments of camera position.
Gitzo tripods, or the old ones at least, are often sold without a central column. You might consider placing a levelling head between legs and head, instead of a central column.
Waist level finders are very good for tripod work and if you focus while really keeping the camera at waist-level while using a tripod they would allow to buy a small and light tripod at least with the normal lens.
I wouldn't use a ball head if the main use is portraits, and I would go for a 3-way head. The choice of ball-head and 3-way head is very "personal", YMMV.
I am very satisfied with my Manfrotto gear: A Manfrotto Triman (#028) which I bought in 1984 with the corresponding 3-way head (#029). This is a large tripod especially meant for studio work, although I find myself going around with it (my avatar was taken with this tripod). I used this tripod with 135, with "difficult" focal length such as 300/4.5 and mirror 500/8 with very good results.
For lighter "tourist" use I have a Manfrotto 460MG 3-way head which I use with some Slik legs of a tripod which I bought for birdwatching (originally fitted with a 2-way head).
I don't think I would consider carbon fibre or Gitzo if not for something "extreme" (extreme portability, extreme weight saving). For a frequent air-traveller, or a hiker etc. it is sensible to go for the best tripods around. For a more normal use I would choose a more normal tripod and spend the money on some other photographic need.