Long story short, how is it? I don't have a DS anymore and it would be a waste to buy one when I will get a 3DS anyways. I have a Wii but it's not really mine. I could play all the Wii games on Wii but to me it makes more sense to have everything on one console. 

Backwards compatibility done right. I believe almost all games should be able to play (DS -> 3DS, Wii -> Wii U).  So get a 3DS considering you are thinking about getting one and you can play DS games on it.

Both are practically 100% backwards compatible with their predecessors.

I heard issues about DS games running on 3DS. Basically is there any issues? Does it look better? etc

DS games run fine on 3DS, but apparently there's colour issues. Far as Wii U is concerned, they stripped out Gamecube BC for no reason. Wii games run.

They took out Gamecube BC on the Wii too, I believe it happened around 2010 when colors started appearing. It was and is to save money as a slot loader is much easier (cheaper) to make that only accepts 1 size disc instead of two. I still have my Wii if I want to play the 3 Gamecube games I still have (ie. didn't get rid of) but with Wind Waker getting an HD remake I'll be down to two :) (hoping Wii U's VC eliminates those as well). The only thing I don't like about Wii U's BC is you have to load the Wii Menu app, which really just restarts the Wii U into the older Wii's OS and from there you are literally playing a Wii, 3DS's BC is better, you can pop in a DS cart and run it just like you would a 3DS cart and if you imported stuff from your DSi like I did it runs the same as stuff you downloaded on your 3DS, pretty seemless and more than I would expect from Nintendo, the Wii U BC is closer to what I would expect but still wish it was more seemless.

How much money could they possibly be saving?  I still never understood Nintendo's problem here though.  Even the WIi had to restart to load GC games, which is stupid, they're both the same architecture.  It's like me having to restart my computer everytime I wanted to play Quake.

I haven't noticed any color issues. I've been playing all my DS games on my 3DS, and it's been fine. I currently keep my Pokemon game permanently in the game slot while I download my 3DS games for maximal game-age.

I won't pretend to know the specifics of the monetary savings but its obviously enough that they felt it was worth it, plus not having the Gamecube controller ports and Gamecube memory card ports, I bet it came to a tidy enough sum per unit to save them a few hundred million dollars.

As for having to restart it makes sense if you realize that the Gamecube/Wii/Wii U all run different Operating Systems, for another example I have an iMac running OSX but dual booted with Windows 7 (which both run on x86 intel architecture - the versions I run) - I have to restart the computer to switch between Operating Systems because I don't want to pay the extra money to buy the software required to have on of the OS's emulate the other. The Wii/Wii U situation (and Gamecube/Wii situation before it) I imagine are similar as they are running totally different OS's despite the similar look of the Wii/Wii U Menus.

The only way that makes sense is if they stripped OS functions out of the newer OS's.  While possible, it'd make sense just to leave those methods in the newer OS.  While I agree about the ports, that didn't stop Sony with the PS3 to use the HD and PS3 controller (early PS3s had the PS2 inside of it) for PSX/PS2 games, and I can't see Nintendo's engineers being that incompetent to not be able to do what Sony did and use/remap the GC controller to the tablet and saves to the HD in the Wii U.