How quickly can it be done, and how much money should I intend to spend?

Typically it may take 4-5 months to have all the paperwork executed; I am allowing a generous amount of time to deal with the father issue. If the father is known and locatable you will need to provide him notice of the intended adoption. if the father is not known, you may need to serve by publication. It would not shock me to have a quote of $2,000- $2,500. Best of luck to you.

Is it possible to do an adoption without a lawyer?
The baby has no father. Unfortunately my sister went a little crazy after our dad died and ended up pregnant with no idea as to who she slept with.

What would I need to do if I wanted to go through with the adoption without an attorney? What paperwork would I need and where do I file it?

In most states you would still need to serve by publication for the father. This is done by publishing an ad in the local newspaper. I am not sure about the requirements in Kansas but it Florida it must run for four weeks. You would indicate in the ad that this is a "John Doe" situation. I would contact the Clerk where you live for more instructions. Best of luck to you.

Would it be the same process if I pursued JUST custody?

Thank you for all your help, by the way!

If you pursued just custody of the child you are probably looking at a guardianship but you would still need to give notice to the father, again by publication.