Some people install Apple Bonjour on their Window system, you could try that and see if it works.
Of course you could, as a quick-and-dirty-fix, add a line to your HOSTS file, but that would be only helpful if the IP of your ESP doesn't change.
When you're new, don't start with a separate ESP (ESP-01 to ESP-14) module.
Get yourself a proper development board: NodeMCU - WeMos D1 - WeMos (UNO form factor) - Witty Board
ESP power requirements are 3.3V±10%@350mA
The ESP8266 IS NOT 5V tolerant on ANY pin (see item 5.14 on page 25 of the FAQ)
For the time being I'm using static IPs. I had done some work using mDNS to do a discovery of IP addresses and to then store those IPs in the device that needed them. (for ESP to ESPs com) After that point use them as static IPs until they disappear and then do a new automatic discovery. I found that mDNS was too slow when it worked. I still have more work to do on this but I haven't been able to get back to it. Too many projects and not enough time.
mDNS will not work with the webserver in AP mode. You will have to use a captive portal. See this example https://github.com/esp8266/Arduino/tree/master/libraries/DNSServer/examples. In the example the portal captures all web requests and redirects them to the softAP IP. So just change the "*" with your preferred server name. Also in my experience, I had to abandon the .local address. I just went with a different domain like "esp8266.io".
Hope this helps.