welcome to Fuji X. it's an interesting world, photographically. I have enjoyed my experiences, personally. I started with the X-100s - which is dear to my heart. A nearly pure photographical experience - where gear nearly becomes transparent. it's a very different experience. I've since added the X-T1, a capable addition adding compositional flexibility - which, my 2c, is sometimes over-rated.
I would not encourage converting Canon EF lenses to the Fuji X mount. Two reasons: first, the whole point of a rangefinder or even mirrorless in general (often?) is compactness and an unobtrusive influence at the setting and in an image.
Canon EF lenses - save the two pancakes - are not compact - having distinct tendencies toward massive.
Secondly, EF lenses do not have aperture rings. Thus stopping down is nearly impossible via Canon's electronic EF lens to body metering system (there are no electronic communications with a Fuji body). I've heard of stopping down by placing an EF lens onto a canon body then stopping down the lens in manual mode, then remounting to a fuji adapter/body - but I've not tried it. Seems too convoluted and time-consuming.
while I believe a few EF->F adapters have an independent (in the adapter) step down ring (metabones has a 0-7 scale) it's still - my 2c - not conducive to my preferred methods of shooting. besides, metabones are not cheap.
fuji's xf lenses are very good to excellent and they fit (size wise) your camera. however, they are not cheap - save a few of the more modest offerings, like the previously mentioned 18-55 (circa $400) and the 27mm pancake (a cool little eq 40mm).
alternatively, consider adapting one or two older manual focus lenses to your Fuji. As the X-E1 isn't noted for its AF prowess anyhow, many fuji shooters actually prefer using manual focus. your control is significantly better (imho). consider these lenses with aperture rings - as you can then stop down - which, normally, you'll probably stop down 1 to 2 stops for corner sharpness & vignetting. Examples include: m-42 lenses (some nice affordable Zeiss offerings and their russian cousins - helios, etc.), Pentax Takumars, Minolta Rokkors (love my EF-converted 58/1.2), Canon FD & FL lenses (some are really nice & some are still pricey! - propped up by their current demand as desired lenses for mirrorless bodies), and even - gasp - lenses from the Dark Side (I presently have a 55/2.8 micro nikkor adapted on my X-T1 - a cool macro lens that doubles as a EQ 75mm portrait lens).
many such adapted lenses - still a bit larger than the native fuji XF lenses - are very economical - even thought the prices seem to be increasing.
again, lots of choices for you to consider. maybe try a single adapted manual focus lens. I think you'll be pleasantly surprised with the experience.
good luck, and have fun...
Dale