I like your thinking Eruvanda. There are two details that I'd consider very important, and a slew of other minor things.
First, how long do you think it will take you to save up? The area where I live (two mid-size college towns) is a very rural/agricultural region with housing costs driven up by the large student population--a bedroom in an apartment goes for ~$3.6k+/year (ie $300+/month). If you think you could save up for your big yurt within a year, it may be easier to rent an apartment for that time (depends on costs, etc).
However, in an apartment you won't get a chance to start experimenting with the many basic yurt living systems--water source, water disposal,
[space & water], cooling [if needed], lighting, cooking, storage, toilets, garbage, etc. This is not something you want to just jump into blind--standard practices don't directly transfer to yurts very well. Winter is not the time to figure out you need more insulation/heating so your water doesn't freeze overnight, creating a plumbing leak that in the morning thaws & shorts your nearby electrical cords and starts a fire (really bad hypothetical situation).
The next big question is do you have a place to setup your yurt or pre-yurt? Once I decided I wanted a yurt, it took me several years to find a location (and even then I can't live undisturbed in the same spot for more than 6 months due to county code). Having a place where you can rent a room plus setup the yurt would be ideal--you can work on your platform while saving up for the yurt, then move into the yurt in the spring/summer but still have an emergency backup living plan while you get hands-on experience with the slew of yurt living systems before winter comes.
For your other question, there are wall tents, some traditional yurts,
, cargo containers, RV/camper trailers and many other things that could fit the bill of a cheap dwelling (<$5k) while saving for a nice modern yurt. My ~20 ft yurt cost me ~$3k with shipping from Budapest to Seattle (no insulation). Smaller spaces loose less heat, but
cuts the heat loss; drafts steal a
lot of heat. Of course you'll want to figure out the snow loads for your location and how any dwelling would handle it.
Hope that helps!