I'm relatively new to the game, and I started with Colette's crew.
The game is mostly easy and quick to learn. There are some rules tangles that can trip you up along the way (getting used to how triggers work took me a few games) but for the most part the rules are well written and clear.
Arcanists as a faction isn't really something you learn per se - each master is quite individual and their playstyles are very different.
Colette takes a little bit of getting used to. Her playstyle involves lots of trickery and movement rather than brute force, and her minions are mostly pretty fragile. However, I found her ability to generate soulstones during the game made her a little more forgiving, and her crew's unbelievable mobility makes getting position-based objectives easy. Stick to the mission and avoid direct confrontation and you should be fine. These boards and the PullMyFinger wiki have plenty of tactical advice for Colette, and in my opinion learning with her gives you a better grasp on the rules than if you learn with one of the more straightforward masters.
I don't know how prices translate (I'm in Australia) but a basic 35ss crew runs to about AU$70 for me. That's enough for a decent-size game, or several options in smaller games. For Colette, you need the box set, a pack of Doves, and a pack of Coryphee.
It's easy enough to get other people into the game (I've been dragging my friends in pretty easily) especially if they're looking for a change from GW games. There's enough variety in the masters that anyone should be able to find something that appeals.
That said, I don't think the Colette crew is very good for teaching games. The Showgirls have so many tricks that the opposing player tends to get frustrated, especially if they're running a melee-heavy crew like the Viktorias. Their abilities are also complex enough that it's not obvious how they work without a bit of research and planning, so you can't just give them to a new player completely cold, either. Personally, for learning games I'd recommend the more straightforward crews like Perdita, the Viktorias, Nicodem, Rasputina and Lilith.
As mentioned, the Arcanists don't really have a single playstyle, and there's not an awful lot of synergy between them for Brawl games - I'd recommend Ramos if you're looking to expand. Colette's crew combines a lot of mobility with a couple of decent melee damage-dealers, spell damage, debuffing, luring, poison and some surprising resilience, and their main advantage is that almost the whole crew can gain the ability to use soulstones. Soulstone management and movement tricks are therefore the main aspects that you have to learn.
Starting with the Showgirls has been fun for me, so I hope it will be for you also.