I’d go for a custom PC build. You can either build this yourself or have a shop build one for you. I have never build a PC before and with some patience and YouTube-videos didn’t have any problem doing it myself.
I personally think that at about $1000 total there is “sweet spot” for a computer for music production. Obviously you can spend a lot more, but the money spent to get small improvments will start to grow at this point.
Now concerning the parts and what to look for:
CPU: This will be the most important part of your computer when it comes to music production. If you want to run several tracks with some software synth and effects on them you’ll want some power to calculate. I’d aim for 4 or 6 cores. Keep in mind that most DAWs (like Live) can not calculate any track on more than one core. The i7-5820K would be my pick. It has 6 cores at great speed. At about $380 this is probably the most expensive part of your computer, but that’s what you’ll want. You could consider the 5930K for $480, but I think that’s not worth it.
CPU cooler: Since you will want to use this for music production you’ll want the computer to be as silent as possible (and affordable). Therefore you’ll want something like a “be quiet! Dark Rock Pro 3” or similar.
Motherboard: First of all the motherboard needs to have the fitting socket for your CPU. So depending on the CPU you choose you’ll have to chose a suiting motherboard. Same goes for your RAM. The new DDR4-standard needs a new motherboard that ideally also supports a higher frequenced RAM. Also you’ll want to have some onboard connections (LAN, USB 3.0, etc) and some slots for additional PCI cards (graphics, firewire, etc), but 99% of all remaining candidates should have those.
RAM: 16GB should be the way to go. Even though it’s a little more expensive I’d go for the faster DDR4 standard. I’d go for something with a little more than the standard clock speed.
Storage: For storage you’ll want some 256/512GB SSD. You can usually go for a 256GB one when on a budget since usually it’s very easy to just add a second or even more drives to a desktop computer.
GPU: Even though running Live is not very graphic intensive you might want to consider buying a small graphics card. The i7 CPUs have a graphics card built in, but to reduce heat here and to add a second monitor I personally would add a small graphics card. The Palit 750TI KalmX is a nice pick since it does not need active cooling. No fan, no noise.
PSU: For the power supply you’ll again want something that is as quite as possible since this part has fans as well. Depending on the exact parts you chose might want to not chose the smallest one (500W or sth), but you won’t need a 1200W one either. The Dark Power Pro 11 Series by bequite! is a safe pick here. Also they are modular so you can add/remove just the needed cables, which grants flexibility and improves air-flow in the system. (Air flowing nicely=lower temperatures=fans going slower=less noise).
Case: I’d look for an isolated case. I personally use the bequite! base 800, which is not exaclty the cheapest, but the additional isolation is really neat. However Corsair and Coolermaster also have some cheaper options.
That’s pretty much it. I personally run a custom windows PC and I’m very happy with it. I have a MacBookPro as well, which however gets to it’s limits quickly on bigger projects so I only use that on the road. I can only recommend building your own PC and picking exactly the parts you want/need.