Welcome to the hobby! The X-T20 is a great camera.
> also there is a unique "look" that the Fuji mirrorless cameras spit out due to their x-trans sensor[1]
The performance of the Fuji sensors aren't the main reason behind the processing, for sensor type comparison, there's a great article here:
https://medium.com/@nevermindhim/x-trans-vs-bayer-fantastic-...
Fuji cameras have built in post-processing that allows it to render images closer to film stock. Fuji has spent a lot of time refining their post-processing to match how it would like across their own film stock and really the only manufacturer that achieves such a great out-of-camera processed images.
If you are working and shooting in RAW, you'll find the output from Fuji when processing the RAWs yourself are not much to look at when you look at a RAW file in RAW processing tools like DarkTable etc. They're fairly similar really to any other camera mirrorless or DSLR. You'd really have to be pixel peeping most of the time to really see a noticeable difference (assuming lens etc. is very similar). When working in RAW, you can often get similar processed colours and images out of most cameras so really this shouldn't be a limting factor. From my Android phone, I can save RAWs and generally achieve similar colours and overall appearance etc. Although, due to the sensor size, it will be notably lower quality if you start pixel peeping and generally the colour depth is usually less to work with on mobile sensors.
Edit: Had the wrong link for the article.
