It definitely depends on power usage. My HTPC can be powered by my solar panel because it is undervolted and draws 30-40 watts. I currently have a N3150 Celeron and my N3700 laptop powered by my solar panel, along with running lights and charging boost packs for powering my phone and Bluetooth earpiece.
Solar panels are very affordable, so it doesn't make much sense to spec it out and get the bare minimum. Just making up fictitious numbers here, but if you found you needed just over 200 watts of power for a typical day, I wouldn't just get one panel ~250 or two that add up to that. I would get 2 x 150 watt or 3 x 100 watt panels. Maybe more if I could afford it.
You would have to go outside and survey where the sun lands and what obstacles might be in the way, also noting what may grow into the way in the future. You need to be able to survive cloudy weather on the winter solstice. As long as you can survive that then you won't have any problems. Cloudy days still give some power. My batteries are full now even with days of rain because my load on it isn't that high. I probably get almost as much energy on a mostly cloudy day in June than a mostly sunny day in December.
There are lots of options for batteries. Shipping can kill an otherwise affordable deal. Amazon has a few things, or you can hunt around locally. I've heard of places dumping old UPS's with big batteries that can be salvaged. Sometimes people make setups of a similar size as what you need and can buy the whole thing for a reasonable price. I have a pair of 50AH batteries from a wheelchair. It isn't perfect since they were used gel-cells, but free and still taking a charge over 4 years later.
I would avoid the Harbor Freight Panels or the long rolls made for roofing. They are amorphous and only last around 10 year vs mono- or polycrystaline panels which usually are warrantied for 75% to 90% of rated power after 25 years, depending on manufacturer. Also the manufacturer of those amorphous roof rolls went out of business, plus I think they are 24V.
That could be an important point. The voltage of the panels and the charge controller have to be compatible. Going with a higher voltage setup means there will be a larger difference in voltage between the battery bank and the computer, which means lower efficiency. It would likely be best to stick with 12V or maybe 24V.
Then of course if you expect to run an overclocked high end CPU with a modern high end video card then good luck finding a power supply. In that case you might have to get an inverter. This means more inefficiency. The same rule about battery voltage applies to inverters. A 12V bank converting all the way up to 120V would be less efficient than using a 48V bank, and that would be less efficient than a 96V bank, assuming you can find an affordable inverter that accepts the voltage you want to use.
I personally believe in using cheap charge controllers for small scale solar and buying an extra solar panel vs buying a massively expensive MPPT charge controller, unless you are not stationary. The increased efficiency just isn't enough to cover the massive cost increase for a good MPPT controller. It's cheaper to just grab another 100 watt panel or whatever you are using and end up with more power, not to mention the panel will last much longer than even the best charge controllers that I have seen. I'd also really like to see a side by side comparison of both setups in low light conditions, as I think having more panel surface area could be better at collecting light (energy) in that instance. For mobile uses you need the smallest and lightest setup possible, so monocrystalline panels and MPPT would be better.
If you just want to offset your energy usage and lower your power bill then just getting panels and a grid-tie power inverter would be much cheaper and easier. With the relatively cheap cost of panels you can make back all of your investment in a handful of years or less.