Medical Prep Needed to Bring Stray Inside?

My question is basically, what medical needs have to be taken care of in order to safely bring a stray inside so that my already indoor cat isn't at risk of exposure to anything?

This cat showed up at our house about 9 months ago, she had a clear collar mark when she first showed up and she is microchipped but it is unregistered. We're finally preparing to adopt her in full (we've already been feeding and sheltering her the entire time) and bring her inside, especially with the cold coming in.

I really think she's had an indoor home before, she is always trying to come inside, completely at ease indoors when she does let herself in before we boot her out again, and even used my cat's litterbox once (no one realized she was inside and I thought it was my cat I heard digging around in it, but my cat was in an entirely different part of the house). She appears in good health (except for an injury (scraped nose) she sustained very recently that appears to be healing up nicely).

We just need to know what all is necessary to have done to make sure she's safe to bring around Indoor, and to get an idea of how much all of this would cost.

(I'm thinking this cat wasn't much older than 2 when she showed up (I've never aged cats before, but her teeth struck me as soon as I saw her,  super pretty and white, which I hear was a two and under thing), and Indoor approximately just turned 10.)
 

Thanks for any advice!

Any other tips about taking in a stray would be welcome, too. Never done this before.

The cats occasionally have come into contact and sniffed noses/necks and seemed fairly fine with each other. No obvious aggression or tense body language. I would push them away before they actually started to touch, though, since I was nervous about health risks.

The very first step is getting the cat to the vet.  You need to be sure she is spayed and is up to date on all vaccines as well as being tested for Feline Leukemia and Feline Aids.  You do not want her having contact with your other animals until she has been seen by the vet.  She will also need to be wormed. 

When you bring her inside, she will need a room of her own.  This room will need to be cat proofed.  If there is a bed in the room it should be picked up or laying flat on the floor.  Under a bed is the first place a cat will run to hide and it is nearly impossible to get them out.  Also block all other large furniture.  Cats can squeeze into very small places. 

Be sure to have 2 litter boxes to start with.  Also provide fresh food and water.

The new kitty and your resident cat should not have contact for awhile.  The new kitty needs to adjust to indoor living first and adjust to you.  You want to be able to touch the kitty and hold the kitty first.

When the cat is comfortable in the room of it's own, you can cstart cat to cat introductions.  This can take a few weeks or many many many months.  Cats are territorial and do not take to each other quickly.  Introduction processes take time and patience, but are necessary for the safety of the cats.

Here are a few articles on the introduction process

http://www.thecatsite.com/a/the-ultimate-yet-simplified-guide-to-introducing-cats

http://www.catbehaviorassociates.com/a-simple-little-trick-to-use-during-new-cat-introductions/

http://www.aspca.org/pet-care/virtual-pet-behaviorist/cat-behavior/introducing-your-cat-new-cat

http://jacksongalaxy.com/2010/10/01/cat-to-cat-introductions/