It seems to be ideal for gaming whereas I need for audio production.

Ya judging by those specs that's gotta be an old  IDE type laptop drive. Not worth spending money on. and if the RAM is not DDR 2 SODIM or newer you won't even find it.  
 
I'm not an experienced builder and if you lucky mabey one of those guys will chime in, But most of them sell pre built systems for a very reasonable fee which is a smart way to go if you don't have a lot of comuter knowledge at this moment. And by the time you learn every detail of what's available right now, something new will come along that makes it obsolete. But that said, you can save a lot of money bilding your own and for me it's part of my ultra nerd personality that makes me go there.
So the follwing is just what I did and by no means the right way to do things,,, but it worked. 
 
First you'll see that most Mobos are  gaming ( crossfire) and the price goes up accordingly. 
What I did was start at the lowest price point for 1150 intel and 97 ?  ( $ 79)  and work my way up, I made sure it supported all the things I was going to plug into it. Make sure it has 3 video options, 6 USB 2 ports 4 USB 3 pots etc. I also looked for the orientation of the SATA ports.
The processor you get what you pay for so just set a budget and make sure it to is 1150.
Memory is going to be $160 for 16 GIGs. You could start out with 8 and add latter.
 
There's more but I gotta run..  
 
 

audiomyth where are you based?
 
If you live in the UK, try www.scan.co.uk or www.pcspecialist.co.uk who will be able to advice you. Specify what you need it for. SSD, fast reliable storage and good external options - USB3 or Thunderbolt.

One of the first comments I picked up on was that your budget was "economy"...so I would be looking for a middle of the road solution. I agree with the other poster that the Intel i5 is a good intermediate way to go. I would also consider AMD. Without getting into too much detail AMD is ok and slightly slower in just about every application, but not significantly slow enough to stop it from being a good contender in the middle performance brackets. In my opinion the only reason to go AMD would be purely economic because you should be able to land an Intel i5 and the motherboard for about the same price....don't let the number of cores fool you in AMD...the actual performance of a 6 core AMD isn't really any better than a 4 core i5 chip. AMD chips use more current and give off more heat for the same return .vs Intel. ...You still might find a bargain in AMD you can't pass up and if you're on a budget you could do much worse than  a 6 or 8 core AMD chip.
 
The older socket configurations and chips from intel, both i5 and i7 are less expensive than the latest offerings....and they can still scream with the best of them in terms of speed...plenty for DAW work.
 
Although you can spend $ 1000.000 as of this writing for an 8 core intel chip...minus MOBO or anything else there are some intermediate bargains out there that might fit into some budgets and get the job done. I am building a system based on the i7-5820K. The chip is over clockable...but when you jump into that arena everything will cost more...you need a good power supply. The chip needs 3rd party cooling and the MOBO costs more than the older socket mobo.The most recent socket is the 2011 v3 and the MOBO configuration is X99...anything in this range will cost more...I still think it's a decent entry into more than four cores. I got my i7-5820K for less than 400.00 and I think 6 cores is probably overkill for my studio....but it should be good for some time to come . I plan to have at least 16gb of memory and at least one SSD...it all adds up though. You can do an AMD system in multi core or an i5 for much much less and probably get by fine for most studio work.