Which console to buy for Rock Band 3
Solution 1:
I'll try and tackle all parts of your question in the order that they were listed.
Hardware capabilities:
Graphics: In this respect, the PS3/Xbox 360 are better as both consoles support resolutions up to 1080p, while the Wii is capable of a mere 480p (and that's SD as opposed to HD). Resolution aside, the PS3/Xbox 360 also have superior processors which obviously allow for better looking games. With Rock Band 3 in mind, just compare this (PS3/Xbox screenshot, as the game looks more or less the same on both) with this (Wii screenshot).
Sound: Other than the hands-on differences mentioned in Jason's answer, consider the following fact: Both PS3 and Xbox 360 are capable of digital audio output, while the Wii is, as far as I understand, only capable of Stereo output (not owning a Wii, I rely on the manual, specifically pages 6 and 8, and this support page stating the console is capable of simulated surround sound).
Instruments:
This is something I know very little of, but browsing through the official shop makes it look like there are plenty controllers available on all platforms, all looking more or less the same, at least physically.
DLC:
All consoles are capable of downloading additional songs (see the official instructions for the PS3, Xbox 360 and Wii). The only consideration is storage space, so I wouldn't recommend something with just 256 MB of it, as I assume (couldn't find specifics) that new songs will weigh about as much as they did in previous games (~40 MB).
I read on the official site (though the link eludes me) that songs on the Wii are stored in SD cards, so there's no need to worry about the Wii's limited storage capabilities.
Just remember that the region of the game you purchase (NTSC/PAL) will most likely force you to buy DLCs with a corresponding region. I know this for a fact on the PS3, and imagine it is the same on the other consoles.
Finally, I don't know whether all song DLCs will be available on all platforms, but I doubt anyone knows that for a fact.
Installation:
I do not know if Rock Band 3 requires any sort of installation before playing, but even if it did it could only be mandatory on the PS3, as Xbox 360 should never have mandatory installs (as there were models that had no storage at all. I am unaware if that policy has changed, however) and the Wii hardly has any storage capacity to make an install worthwhile.
Assuming a mandatory install on the PS3, I have never seen one go beyond 5GB, roughly.
Online Service:
Using PSN or Xbox live is not a real issue even in countries which do not support it (more so if all you want is to buy DLC, but multiplayer should also work). In both cases, simply lie about where you live in order to get yourself registered to the service. Since buying things through said services requires you to have a credit card matching your declared place of residence, you'll simply have to use prepaid cards, which are available for both PSN and Xbox 360.
While I know less about the Wii's online service, I do know that it is also not supported where I live, and that the process for buying things is more or less identical (prepaid cards are also available for purchasing Wii points).
This means that the DLC songs available to you will have nothing to do with where you live, but rather with which shop you register to (this is determined by where you declare you live).
Xbox models:
Essentially, all Xbox models have the same capabilities hardware-wise, though newer models are easier to connect to televisions/receivers (older models didn't have HDMI output, if I recall correctly).
Seeing how Xbox live is not officially available in your country, I would guess that the Xbox 360 is not officially sold there as well, meaning you should avoid cases where you have to exercise your warranty. Older Xbox 360s are renowned for breaking down left and right, so you should opt for buying newer models. The new "slim" model (the one that looks like this) is sure to be less disaster prone. Older looking models also had a hardware revision which made them more robust, but telling those apart is trickier. Should the need arise, there are guides and I'm sure you'll be able to find one.
Assuming you don't want to worry about space, I'd also avoid the 4GB model (though using some bad math, you should be able to squeeze around 100 songs on that).
Bottom line:
Rock Band 3 will run more or less the same on the PS3 and Xbox 360, and will look and sound bad on the Wii (which rather beats the purpose, if you ask me). I would therefore recommend either PS3 or Xbox 360, but the choice is entirely up to you and is comprised of how much each device costs, and which extra features appeal the most to you. Some things to consider are each console's game catalog, media capabilities and even the possible purchase of the PS3's move controllers or Xbox's Kinect.
Solution 2:
Most of my reply will be based on Rock Band 2, since I haven't had the chance to play Rock Band 3 yet.
First of all, there is a graphical and sound difference between the Xbox 360/PS3 versions and the Wii version. Personally, I don't care about the graphics in a rhythm game, but others might, and obviously the Wii does not have the graphical output that the other systems have.
The sound difference is not in the song, but in the additional sounds in the song. In the Xbox 360/PS3 version, when you are doing well, you can hear the crowd start singing along with the song. In the Wii, all you hear is the song exactly as it was recorded. Whether that bothers you or not is a personal preference.
The gameplay between all the versions is identical. However, a deficiency with the Wii is that the controllers are not cross compatible with Guitar Hero, so you are stuck playing only the Rock Band series.
Finally, with regards to DLC, one disadvantage on the Wii is that you cannot copy songs from other versions of Rock Band in order to create a single library of songs to play. If you want to play the Rock Band 1 or Rock Band 2 songs, you have to actually play the older game.
I'm afraid I don't know anything about whether access to Xbox Live or PSN is required for downloading songs. On the Wii, it is all handled from inside the game, but it does require you to have Nintendo Points, so you will need access to the Wii Shop Channel to redeem those.
Solution 3:
From my understanding, Rock Band 3 is basically the same on both the PS3 and Xbox 360.
One downside regarding the Wii version is that the Wii has very limited storage space available. It has 512MB built in (not all of which is usable, IIRC), and while you can buy SD cards to use for storage (up to 2GB), I don't know if Rock Band can load songs directly from an SD card or not.
IMO, I would suggest getting either the PS3 or Xbox 360 version. As for which, I'd say look at other games you'd want to play that are only available on one console or the other, and go with that one.
Solution 4:
I have only owned Rock Band 2 on the Wii, but a major gripe I have is a lack of available content and hardware.
For content: the Wii does not have access to new Rock Band Network songs as they are released. Most of my enjoyment of Rock Band comes from playing the songs that I know. But when Jonathan Coulton, for instance, releases new songs I'm out of luck and can only hope that they'll some day get ported to the Wii.
Source: http://en.wikipedia.org/wiki/Rock_Band_Network
For hardware: maybe this is just my experience and/or region, but I cannot find Rock Band Wii hardware in stores or online. It was a major battle to purchase the set in the first place, and I have given up trying to find an extra vanilla Rock Band guitar. By contrast I see Xbox guitars on shelves all the time.
So my experience suggests that Wii is a second-class citizen when it comes to Rock Band and although I don't currently own an Xbox 360 I am strongly considering buying one just for Rock Band 3. I am of course making the assumption that my current experience with the Rock Band franchise and the Wii will not change much in the near future. Since I imagine my frustrations are ultimately due to business and manufacturing decisions, I think that's a reasonable assumption.