How much would you spend in making your studio if you do want to get into music production?

Well to say something a bit different from what others have said, first and foremost research, read and learn. You can use sources like Youtube to learn more about music production. Also a good internship can help with learning more about music production. In general start within your budget, a great computer, DAW, Monitors or neutral headphones. A lot of producers strictly use the computer, I personally use a lot more tools.
One thing I will say is this, as time goes on you will gain more tools and learn more, however do not be afraid to use whatever you have at your expose. Steve Lacy is a great example, he started producing though his iPhone. It's not necessarily about having more but learning and using what you have.
But research first, and make sure you're passionate about it.

You don't need much. I get a pair of open backed mixing headphones with neutral tone. Then a pair of small powered bookshelf nearfield monitor speakers. Should be neutral as well. Set them up in a space and treat it acousticaly where needed. Moving blankets placed in a wooden frame with attractive cover fabric will absorb a lot of reflective energy. So does carpet. Beyond a computer, DAW, and analog to digital interface that's about all you need.
Check out Presonus. They got a whole line of mixers that can link with a computer and record multitrack simultaneously.
For mics to record with start with some SM58's for vocals, a Beta52 or D112 for a kick drum, SM57's for guitars and and drums. Then 2-4 cardioid condensers for drum overheads and other applications. They should have good low to high end response. Finally get your self some knowledge. LikevModern Recording techniques.
Those Presonus boards can also double as live board with a power amp and pa if you want to mix gigs for bands.

Bare bones. a computer, Audio interface, Digital audio workstation (software).

You can get away with that and do some good, work.

I suggest the following:

• A computer with at least 8 to 12 GB of RAM, with 2 internal drives or an external drive if only 1 internal (the reason for this is that DAW's tend to work better if the disk you are recording to is separate from the disk that contains the computer's operating system and software)
• Audio interface - there are some pretty decent ones in the $90 to $200 range
• A pair of nearfield monitors - I always recommend to my students that the monitors should have 7 or 8 inch cones. The smaller 4 or 5 inch ones give you an unrealistic sound... in other words what you hear in the smaller speakers doesn't usually translate well to larger speakers or headphones, mostly because they don't project enough bass and tend to be overly bright. If you're unexperienced, this causes you to often make unwise decisions when mixing which sound unpleasant when you monitor your final product somewhere else.
• You should also get a pair of good mixing headphones and couple of pairs of closed headphone for tracking (for musicians to use when recording). Good tracking headphones can be costly... major brands have a variety of them (i.e. SONY, Audio Technica, AKG). Be careful of really cheap headphones as they may be uncomfortable, sound crappy and get damaged easily. Of the cheaper headphones I've used that seem pretty reliable and with a good sound are from MONOPRICE.com. They also have pretty decent cables and other accessories.
• Pick up a couple of SHURE SM-57 microphones... these are industry standard and comfortably priced ($80 to $100 each). Beyond that get some condenser mics, a kick drum mic and a large diaphragm mic for vocals. Check out some of the more inexpensive brands like MXL. These mics tend to be a little more delicate than industry standard mics but they sound well and will last if treated kindly. CAD puts out a nice drum mic kit.
•There are several good and not so good DAW's out there. I suggest sticking to the more widely used which have become standard across the industry, like ProTools or Logic Audio. There is a lot of help, tutorials, blogs, third party plugins and accessories for these. Logic Audio is a very complete and interesting tool for composing as it includes a large library of sounds, samples, loops and instruments which make the creative process fun and full of diverse possibilities. I personally have a bit of an issue with the user interface but most people I know that work with it seem very comfortable. It's a matter of choice and opinion.
• Some acoustic conditioning for your workspace is recommended. There is plenty of help out there. Brands like AURALEX have some basic guides for treating your room and there are plenty of sites and blogs with really useful information on DIY acoustics. Beware...: egg crates are NO GOOD...!!!
• I would not invest in a mixing board at this point.

Everything I've said is based on my experience and that of my students. Also, all the gear I've suggested can easily be replaced by much higher-end and expensive alternatives. These however, will get you started. I firmly believe that the right way to learn something is to use the right tools from the beginning. I wish you luck.