The best recommendation I can give is to go for a rig that will be as quiet as possible. Because if you are trying to record an acoustic guitar part or some vocals (which I do as part of my song writing process) you can hear the fan noises or clicky hard drives which can ruin a take or just be a real distraction.
Otherwise, I would say you can save a lot of money off the spec posted by MysteryAngel. You simply don't need that much power to run composition software and digital audio workstations. For instance I run Sonar X3 on an AMD A10-5700 APU with 8gb ram with no real issues. I am not suggesting this is ideal, just that you don't need to spend out for a monster CPU for this build. Your money would better go into silencing the whole rig, having the correct sound card/audio interface adapters to make connection to instruments easier (and less laggy) and considering the software to go with it.
The first thing I would look at is the case. A full ATX case will give you more room for your adapters and allow you to silence the rig easier as they generally allow more fans running at a lower speed leading to less noise from the fans. It is also large and I would only recommend this if you have floor space to stand it. A micro-ATX is a good middle ground where you can install a fair few devices but not as much as the full ATX tower. Again with this you can get a good variety of cooling systems. Finally you have M-ITX which is the smallest but would mean that all the interfaces/expansions you would need have to be USB due to the lack of slots on the motherboards.
At the same time consider how easy it is to silence the case you are looking at. Does the manufacturer have a kit to install acoustic foam is a good question to ask. Best look for reviews on this one, in his latest video Logan mentioned a case that has made his system a lot quieter so that may be a good place to start.
In terms of processor, I would suggest an Intel I5 as a starter. It has everything you need for the job. Otherwise if you are concerned about how your use might grow or recording on multiple channels at once (like recording a whole band) one of the I7 processors might be a better bet. If money start to be a bit hard to balance it might be worth thinking about an AMD FX based system. However that is a dead-end platform in that there will be no more CPU's released in that range. This means that any later upgrades will lead to changing the motherboard + CPU which can easily work out more expensive in the long run. I would shy away from Xeons for this as they are made for server tasks and will not always be as good for general tasks as consumer grade items. They are also very expensive.
In terms of memory, ram is cheap and doing recording work you use a lot of ram. Even if you are just doing midi tracks and using VST instruments to improve the sound, you can use up a whole chunk of system memory. I would start with 16gb and if you have trouble expand to 32gb or even 64gb.
Storage is a real bugbear for most music producers because the cheap storage (traditional hard drives) are noisy and don't provide a smooth/consistent flow of data. That can be a pain when trying to use larger raw audio files (as audio is usually saved in a raw format from DAW programs) causing stutters and possibly de-syncing during a playback/recording point. Thus I would recommend using a couple of 512gb SSD's for your working files and have a separate NAS drive in a different room for your longer term storage. This will improve both the speed at which your data is accessed and keep your system quiet as possible.
Next is cooling. Good quality fans and a manual fan controller is a must. These are quite inexpensive and it is well worth paying that little extra for the performance you gain. I hear good things about Noctua in this area but as before I recommend looking at some reviews for this. I would suggest using a basic water-cooling loop like the Corsair H55 for cooling the CPU so that you can use the exhaust case fan(s) to cool the CPU as well thus saving the noise an extra fan might make.
You don't need a separate video card for this as onboard graphics works just fine for music applications. If you do intend to use this machine for other purposes such as gaming it is worth looking for models that come with a bare heat-sink rather than one that has fans to cool it.
Finally I would say it is best to pay for a really good PSU as this is what will keep all the other components running reliably and stably. Don't be fooled into going by brand names as there are a lot of traps down that road. Take the time to consider your options against detailed reviews and look for a quiet unit that has a good steady power flow. You shouldn't need that many watts going by what you are doing (more than 600w will be overkill), it's simply a point of quality over quantity that you should think about.
There is a whole raft of other things to consider that will effect exactly what gear you need such as the DAW you use and the instruments you use. All of this can be added later as even a basic motherboard comes with various sound (not great though) and input/output options. Cubase is similar to Sonar in its needs are relatively low so a basic I5, 16gb ram, SSD + network storage type system would be more than you need but it is worth considering what you might need down the road.
Most recording studios use Macs simply because that was the best machine for the job in the early 90's and they've never seen a reason to switch (if it ain't broke mentality) so if you are looking to go pro eventually you might be best of going with a rig that you can hackintosh (best look up some forums on which motherboards are best for that) or consider that successful bands such as Metallica use either Logic (which is Mac only) or Pro-Tools which needs a hardware add-on.
I hope this helps.