Great idea! - as long as no one is posting copyrighted material. That could possibly get you and this site in trouble. For example, where did Pro Sound Karaoke come from? It looks like they sell songs on iTunes and Google. But after a bit of searching it appears Priddis Music is the owner for this Karaoke song and it is putting it up themselves on YouTube and if you go to their site this is listed as having a "Standard YouTube License" (the default YouTube license). So here you are likely ok.
But let's talk copyright, which I've been meaning to talk about a number of times here. This is only a general discussion as copyright law is very confusing - so these are just guidelines.
First, what does this Standard YouTube License mean. Basically it lets the owner/copyright holder of a YouTube posting/work say anyone can use the piece on YouTube for personal use (but the owner retains all copyright rights). This is a kind of Creative Commons (CC) Copyright - a new form of copyright allowing people to broadly use things under certain conditions, developed in response to the global web community much of which is based on sharing - but it doesn't say you can use material that is copyrighted any way you choose. Not everything on YouTube is posted legally like this. Normally things legally posted on YouTube are meant to only be used on YouTube. You can not download it and redistribute it unless you see a CC license that allows that. You can also see specific CC licenses posted on YouTube and in that case you need know what they are. So you should never repost things you find on YouTube if you are not sure they have been posted legally to begin with. I'm even starting to get confused myself!
In general, if you buy a symphony album or Karaoke recording or any CD/.MP3 song you can play along to it privately all you like, but that doesn't mean you can legally put it on the internet. It is likely copyrighted material unless it says it's for public use in one of these ways. If you see only this symbol, ©, be careful of what you repost as that is the normal copyright symbol. Anything anyone creates is technically copyrighted the moment they create it. Registering with the copyright office just gives you legal proof of copyright, but you don't have to register anything for a work to be copyrighted (but if you ever go to court, you are likely going to have problems if you did not register it). So if you create something, put the copyright symbol on it with year and your name to be legally safe. If you thinks its great and you are posting it, register it first. Normally you'll see something like this: © 2015, YourName "All Rights Reserved". You can also see things like this: Creative Commons Attribution-Non-commercial-No-Derivs 4.0. This is a creative commons copyright that says anyone can use the piece in any way as long as they don't try and profit from it, nor can then make derivative versions of it. This is the most restrictive CC. There are also CC copyrights that let you use the work any way you like, no holes barred. Again, you have to read the fine print.
If you create your own version/performance of a public domain piece (like Gounod, or likely anything by any composer who died more than 100 years ago) and you want to share it, that's fine. I do that all the time. It's my arrangement or performance of a work that is in the public domain (basically in the US to be safe anything written before 1924 - though there are exceptions). But anything written afterwards is likely still copyrighted in the US. It's more complicated in Europe, where many countries consider copyright is the life of the artist + 75 years (like Italy). That means most all the famous Puccini arias are still copyrighted in some countries and posting performances of them (even your own performance) on the internet can possibly get you in trouble. But likely not. Same goes for Richard Strauss. Salome for example is not public domain in the EU. It's fine in the US - but the problem is when you post something on the Internet everyone in the world can see it (so legally the country where the server is determines the legality of who can put what up). A US site can post the published music of Strauss for example (as long as you are posting public domain scores, not copyrighted modern versions) but no one in the EU can legally open and use it. Silly - maybe but that's the law.
But (barring the CC issues above) taking an instrumental piece you want to use as a theremin accompaniment (public domain or copyrighted) performed by an orchestra or other group that released it and putting it on the internet is illegal without the permission of the copyright holder which is the performer in this case as well as maybe the author (all performances of symphony orchestras even if they are playing Bach for example are likely copyrighted - even if they are performed in a symphonic hall and not recorded - you can't record that as that performance belongs to the symphony). They will own that performance for a long time. Reality? Of course people do this constantly now on the internet for all kinds of performances and put it on YouTube. No one is likely coming after them in most cases - but it is still illegal without proper permissions.
There are also a lot of people posting their versions of copyrighted material on the internet. This is also illegal, though again likely no one will come after you unless you are obviously trying to make $ from it. There are "bots" that do nothing but search the internet for copyrighted music and if found, the owners are notified and likely a commercial will be tacked onto your posting which happens all the time on YouTube (or you could be told to remove it). So the reality is that most likely no one is going to come after you, but legally and morally, it's wrong without getting permission or possibly paying royalties to do it. A good example is I see thereminists posting their version of Morricone's Gabriel's Oboe. I'd like to as well, but I don't see that Morricone gave permission for anyone to perform this work in public without his approval or paying royalties (especially if you don't even buy the music first to do it - then maybe you have at least a little better moral case). So I'm not going to do something like that even though I'm pretty sure Morricone is not going to come after me if I do.
Finally, the notion that you can put any copyrighted material on the internet and then say silly things like "no intent to violate copyright" or "for personal use only" is ridiculous (I see this all the time). Putting things on the internet is basically distributing it to the largest audience in the world. There is nothing personal about it. You are in essence, illegally trying to publish other people's work.
It's a nightmare. But that's the reality. As a composer I am particularly sensitive to this area and I want to respect people's hard work, which they own the rights to.
Now I've actually been working on a number of my own accompaniments of public domain pieces that I use for practicing, and I'll be glad to post them here.