If you're having to ask people for ideas for which songs to pick, I think you're going about it the wrong way.
Basically, I've worked on quite a few music videos, some more professional than others - and the ones that are most succesful are the ones where the director has a clear connection
to the song.
The song needs to make you
feel a particular way before you can try and make anyone else feel anything - and it's not a feeling that you can force, you need to have a strong emotional reaction to the music, otherwise what you create on screen will simply be a sequence of shots edited to a track, nothing more.
What you want, ideally, is a situation where as soon as you listen to the song, you've got a clear image in your mind of the kind of things you want to show in the video. Wether that's just the style you want the video to take, or you actually get an impression of the story you're going to tell, the music needs to instantly conjure up mental imagery for you - if you're having to force that, then how are the audience ever going to have an emotional connection to the video you create?
So, find a song that has meaning for you. Maybe it reminds you of a certain time in your life... Maybe you can apply the lyrics to someone you know... Maybe the song just fills you with energy and makes you want to take on the world... Whatever it is, you'll know the songs you want to make music videos for when you hear them, because something inside you will just 'click', and you'll think - "Woah, this song makes me want to show other people how I feel when I listen to it". When you get that feeling, you know you're working with the right track!
Other advice I'd give you is to really work out the story
of your music video. There's a temptation, when you're making a music video, to simply rely on cool effects and snazzy editing, but if you don't know what the central storyline of the video is, what you create is going to lack depth and meaning. If you don't consider the emotional journey that you're going to take the viewer on, you might end up with something that looks amazing, but again - the viewer has no 'connection' to. And when I say 'story', I don't mean that you have to specifically introduce some characters and have them do something - it doesn't have to be that literal (but it can be if you want!). But you have to know what the meaning of the video is, what the message is you want to give to the viewers.
Also, there's no better source of learning for music videos than by watching, plus it's a great excuse to watch loads of em! Here are some of my particular favourite music videos, all for different reasons. If you get time, I'd reccomend you watch all of them, and consider how they make you feel. You might know some of them very well, you might never have seen them - but either way, watch them, think about what the director's message is and what he's saying about the music. Also, this isn't a list of the 'best' or 'greatest' videos ever, just ones I really like (and I can think of at the moment!):Radiohead: Just
This video is really intriguing, and it blends the mixture of storyline and band performance really well. The Avalanches - Frontier Psychiatry
Completley different to 'Just', this video is really silly, but great fun to watch. I love the way the director has represented all the different samples and elements of the music with different characters. A very simple set up used to great effect.Sinead O'Connor: Nothing Compares 2 U
This video is a pure classic - it's an emotionally charged song, and the way the director has used simple, intimate shots really conveys the feeling of the music.Johnny Cash: Hurt
Again, hugely emotional and moving video - made even moreso as it was the last video Johnny Cash ever made, and you can tell that he knows his time is fast approaching. A great cover, and a really well made video, which is a fitting tribute to a musical legend.Jamiroquai: Virtual Insanity
Another change of pace, this is a really innovative video.Radiohead: Karma Police
Another great Radiohead video, I think this really captures the mood of the song.Royksopp: Eple
Apparently made by using photographs from the band's own photo albums, this is a great visual journey, using a very cool effect.Bronski Beat: Smalltown Boy
A very traditional 80's video, which tells a story that reflects the lyrics pretty literally.Coldplay: The Scientist
Stunning video, using a very cool 'backwards' concept. This video has taken a simple concept inspired by just one line from the song, and makes a beautiful piece of art from it.Daft Punk: Da Funk
Something completley different again - the story almost takes precidence over the song, but I think it works incredibly well. The video and the song have nearly nothing in common, but I think the director (Spike Jonze) has brought life to what could have been a very dull house music video.Peter Gabriel: Sledgehammer
This is a great example of traditional stop-motion techniques, a pure classic.Electric Six: Gaybar
A hillarious video for a very funny song - pretty controversial use of a historical figure, but it certainly sparks an emotional reaction in almost everyone who watches it, making it particularly memorable.Junior Senior: Move Your Feet
Superb animation style that you can't help but smile at.Madonna: Like a Prayer
Another great 80's story video, blending musical performance and the narrative.The Prodigy: Smack my B*tch Up
This video was VERY controversial when it was released - it's still banned on most music channels, in it's uncut form. However, it's a great example of playing with clichés and audience expectations, as well as using a very cool POV style shooting, which makes you identify with the character, wether or not you want to. (18+, you'll need to sign in to a YouTube account to watch this one)A-Ha: Take On Me
Probably my favourite music video ever - it uses a clever animation technique, which is still parodied and replicated to this day, but it also tells a story (a woman's love for... a sexy bloke in a comic... odd when you think about it, but hey, it was the 80s, right?).
Well, that was a LOT longer than I had expected it'd be! Anyhow, I really reccomend that you check all those videos out, if you can, and think about the messages and stories they tell. Three minutes isn't a long time, but you can still pack in a huge ammount of storytelling!
I hope this is useful to you, and I wish you the best of luck with your music video project.