The html5 standard allows for embedding mid files into web pages, and Adobe Dreamweaver does this.  The last GM device still available is the Roland Integra 7.  You can play back mid files using Apple Quicktime.  The question is, what DAW software lets you write mid files in this day and age?  SONAR can do smf files, right?  But mid files?
 
Also, for your curiosity, Hittrax sells mid files.

You can write MID-files with SONAR.
Create a track for each MIDI channel.
Save as type --> MIDI Format 0 and MIDI Format 1
So you have MID-Files.
You can also open other MID-files.

I don't know anything about your background, but your post makes me think that you haven't got that much experience with MIDI. If some of the things I say seem very basic to you, please bear with me. Otherwise, one or two things may be good to know before you start spending money. A Roland Integra-7 is definitely not cheap, but it's also nothing you would need in order to make MIDI files play on your web page.
 
First of all, a fantastic MIDI sound module on your side doesn't mean anything with regard to how that MIDI is played back on someone else's computer. You may fool yourself into believing that what you hear on your Integra-7 (or whatever sound device you've got) will be equal to the sound the end user will hear. It's not. It may sound very much different, as MIDI only contains musical information and not the sound itself. For that reason alone, you will hardly ever find any embedded MIDI files on web pages nowadays.
 
If your aim is to play back some music on your web page, a much better approach is to capture the output from your external sound module (if you've already got one), or optionally the output from a computer based software instrument. Then compress the result into an mp3 file to be embedded. This will guarantee that everyone will hear the same sound that you are hearing.
 
Of course, you would somehow have to record your performance and doing so in SONAR is a good choice. That would also make it possible to use one or many MIDI controlled software instruments included with SONAR which could then be used to generate the sounds instead of an external sound module. Not many people would buy an external sound module today, unless it is to be used on stage or in a professional studio (where you wouldn't want to risk latency or other computer related problems).
 
Still, if this is something you are going to do only once, then I would advice you not to. There are many things you would have to learn and quite a few dollars you would have to spend to create those files. Maybe someone with everything in place can help you? But if music is your interest, then there's really no end to the possibilities.

GM ( General MIDI) sounds are played back using the MS Wavetable synth on PC and then something similar on a Mac.  So no point using anything better, it won't change what other people hear.
So if you want to know what everyone else will be hearing,  you set Sonar ( or any DAW) output in MME mode and use the MS Wavetable as your sound source while composing.  It will sound pretty boring unless you get a handle on the deeper editing using System exclusive coding. Game designers often use midi as the sound scape.
 
 

The Quicktime synthesizer plays them back. 

QuickTime for Windows is not supported by Apple since January 2016. As it is a security risk, you wouldn't find many Windows users having that installed.