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.
Best Answer
You and your friends could also get a router that supports VLAN's as well, and connect that way. But the lag may be a problem.