Before reading: this is all very ballpark and based on my own recollections so YMMV. I definitely may have missed some things.
K1 VISA STAGE
I-129f filing fee - $695
Other fees associated with the I-129F: Official passport-style photos for each of us; mailing and tracking fees for the package
Medical Exam Fee - ~$500
Other fees associated with the medical exam: Travel & lodging if needed to go to the exam center; my now-husband had to pay an additional ~$100 for a Covid vaccination ahead of time; also had to pay an additional ~$100 to meet with his GP to obtain medical records and also to obtain a letter about mental health things.
Will also need separate travel & lodging to attend to the visa interview after the medical.
Visa fee paid when completing DS-160: $185
Then of course there's the fees related with actual immigration. Flights, any moving costs (such as shipping over belongings, doing the work to sell/store other belongings, the work to sell cars, homes, etc before moving). Once here, there will be costs for obtaining driving licenses, your wedding (whether you do courthouse or a full ceremony there will be costs to this), any living costs - I would estimate we probably spent $2k on moving and "settling" costs.
ADJUSTMENT OF STATUS PHASE
Fees for the adjustment of status package include:
The I-485 ($1440)
I-765 (Employment authorization, $260 when filed with the I-485)
I-131 (Advance Parole if desired, $630)
If for some reason you need to also complete the I-693 (only necessary if your overseas medical exam has expired or was incomplete), that can be an additional ~$100-500 depending on your local civil surgeons and what they charge.
In addition, as others have mentioned, you'll need substantial savings to be able to support 2 people on 1 person's salary when they first move, as they won't be able to work until they obtain their working document or green card, whichever comes first. Then taking into account the time it will take to actually get a job. My husband moved in June, we obtained his EAD in late October, and he had a job and started working the following February. So this was me supporting us, with the help of savings, for 9 months. We also had to purchase a car for him before he had actually started working so that he could get to the work, so, again, that down payment had to come from my salary/our savings.
MATH
SO - by my math, the "official fees" (filing fees, medical exam, visa fees, etc) is somewhere around $3810. That would be the absolute bare minimum.
I would ballpark that, for me, travel costs for the medical, visa interview, and moving over here were probably an additional $5000.
I'd budget maybe another $1000 for those random incidentals - stuff like if you need extra vaccinations, shipping costs, etc. For us this also covered our wedding, which was just courthouse so it was only those fees.
All that stuff together - $9810, or just under 10k.
Then, for us, a solid 9 month emergency fund in savings was necessary from the time he moved here until the time he was able to work. (I was still working, of course, but we budgeted as if I wasn't in case the worst case scenario happened.) We didn't run through all the savings we had budgeted because I was working, which left us with a good nest egg to buy a house at the end of all of this.