So you're getting your feet wet in VFX. Let's start with Software since it's a bit of a shorter list. The software landscape is always changing, but this is a fairly vanilla setup for the typical studio.
Maya - Animation, Rigging, Pipeline Tools, Rendering.
Houdini - Character FX, Procedural FX and Dynamic Simulations.
Nuke - Compositing
Mari - Texture, Look-dev, Shading
Substance Painter - Texture, Lood-dev, Shading
Zbrush - Sculpting, Remeshing
There's a whole other list of software that we also use, but to keep things simple stick with the list above for now.
Hardware is a bit tricky to answer. Yes it's a good idea to be mobile, but for the same amount you can get a much better workstation. The bottom line is, if you can play modern video games within your system then it will probably be good enough to do student work.
Hardware requirements are always changing it's easier to give you links to the "recommended hardware" for the software you will use at home. Using the recommended gear from Maya & Houdini are the 2 big ones, so aim to get gear catered for those 2 resource hogs.
https://substance3d.adobe.com/documentation/spdoc/technical-requirements-172824034.html
https://www.foundry.com/products/mari/requirements
Something worth mentioning is the difference between a gaming machine v.s. a work station. Why do workstations cost more and it seems like the specs are not as good?
Gaming rigs are designed to go fast and be as cheap as possible. Workstations are designed for stability and long term support, but are more costly. In an Enterprise scenario, it is in your best interest to get the most stable hardware to minimize downtime. My workstation is over 10 years old and it still works!! For further reading you can follow this link: https://nerdtechy.com/workstation-vs-gaming-pc
What do I use for teaching? As mentioned earlier, nothing super modern. I use 2 machines, just in case!
UBUNTU
Dell T5810
3.5ghz Xeon (12 core)
128gb ram
RTX 3060 (12gb)
2tb+ nvme
Samsung RG90 5120x1440
OSX
MBP - mid2014 - Big Sur
2.8ghz i7 (Quad core)
16gb ram
Intel Iris & GeForce GT 750M (2gb)
250gb ssd
Retina 2880x1800
The mac book pro can barely run houdini due to graphics card limitations. It's not a good benchmark