If you are using an Android or iPhone to film, then the $60 Røde Smartlav is hard to beat.
It sounds great and a lav clip-on mic overcomes a lot of issues with recording at home.
If you want to plug a mic into your computer a digital connection is best.
The USB port on your computer is digital, for example.
If you want the absolute pro sound, you need a pro mic - These are the ones with a three-pin XLR connector.
You attach a pro mic to an interface like the iRig PRO and your production values jump significantly.
The iRig Pro attached to a Rode NTG-1 shotgun Microphone.
This interface converts the analog audio signal from a pro mic into digital one your computer can use. Plus, it let's you adjust the gain (volume level) and even give phantom power to the really, really nice-sounding condenser mics.
You can attach an iRig Pro to an iPad, iPhone or ANY computer's USB port.
I use the iRig Pro because sometimes I want to use a shotgun mic on a boom to record me while I am at my desk (And I don’t want wires getting in the way, at other times I want to attach a wireless mic (for when I am walking around demonstrating something). A other times I choose a sweet radio mic like the Neumann TLM 102 for when I want to give my screencasts a glorious, rich sounding voice track.
I may also sneak in a Joe Meek Mic preamp between the Neumman and the iRig Pro so that I can have some mild compression and limiting on my mic levels. That is a pro audio solution and pro audio upgrades the quality for all of your videos.