How do I affordably and properly change my MacBook Pro's battery?

This link takes you to Mac repair service and cost estimates. For an estimate go to the bottom where it says Get Estimate. Enter your Mac's information. What you see will depend upon where you live so it makes sense for you to do this and not us.

Mac Repair & Service - Apple Support

Since Retina Macbook Pros appeared in late 2012, the battery is no longer a user-serviceable part. If you want "properly," and do not want to be overcharged for it, let Apple do the service.

The estimator on the page Limnos links shows they still service batteries in Early 2015 Macbook Pros.

You have no options other than Apple's proprietary MagSafe 2 power adapter. I've heard of some aftermarket equivalents, but I wouldn't trust any of them. Some recommend going for the most powerful version available since Apple tends to charge the same price with the idea that the supply should run cooler if it isn't used that deep into its rating.

Allan Jones wrote:

Since Retina Macbook Pros appeared in late 2012, the battery is no longer a user-serviceable part. If you want "properly," and do not want to be overcharged for it, let Apple do the service.

They haven't considered any Mac battery to be user serviceable since the Unibody MBP models. I think the last Mac sold with batteries that Apple considered user serviceable was the 2008 UniBody MacBook. That didn't even require any tools - not even a quarter.

But theoretically Apple does allow official user-serviceable battery replacement on some Macs through the Self-Service shop. But they only sell complete top cases with batteries and don't have an exchange value for the returned top case that's would make the price anything close to Apple's battery replacement service that's basically a top case replacement/exchange. I looked it for a 2001 14" M1 MBP and it's $527 or $439 after an $88 return.

Use the Apple supplied charger or an identical one from apple.com.