When I GM shadowrun, I usually consider there to be four categories of contacts. Sometimes they overlap, and sometimes a contact might belong to more than one category, but it is a useful mental construct for me.
First there are information contacts: people whose primary use is that they know stuff. Police officers, university professors, street informants. These are the guys who are good for legwork. Then there are gear contacts: people who can sell you stuff, or fence stuff you want to get rid of. Black market dealers, used car salesmen, fences. Good for swag. Fixer contacts: people who know other people. Fixers of course, but also your mob contact who can get you introduced to the higher-ups. Most fixer contacts will also be information contacts. And finally runner contacts: which are actually other shadowrunners, or at least stand-ins for such. People you can call upon if you need another hacker, a sniper to cover your exit, or a wheelman to get you out of there.
Personally, the only one of these contacts that I would give stats (at least at the start) are the runner contacts, and even they would probably be barebones. The hacking skills for a hacker contact, Stealth and Longarms for a sniper contact, and so on. For the rest, I'd just make a judgement if a roll comes up, using the ratings on page 131, and write down the skill rating I've given the contact at that point. So if the character is asking his beat cop contact about local gang activity, it seems reasonable that the cop would be rating 3: competent in that area of knowledge, if he is streetwise. I also know that 3 is an average attribute. Our beat cop has been established as a bit smarter than average, so we give him 4 Intuition for a total pool of 7.
Of course, I have a tendency to throw loads of contacts at the players. If their fixer introduces them to a fence, I'll give them the fence as a contact with an appropriate Connection rating and a Loyalty of 1.
A lot of the time, however, I won't make any rolls. In most cases information contacts will know just enough to let the players make informed decisions, but not enough to do their work for them. Our beat cop would probably know if the Halloweeners are on the warpath, and there is also a decent chance that he knows where they hang out. What he is unlikely to know, is where they have stashed that girl they just kidnapped. Of course, if a player has a Halloweener contact, and can get him to talk, he would probably know that, unless there is some reason it would be kept from him, in which case he might just have an idea about likely places. My advice is to not use the dice (or bribery guidelines) too much when playing the contacts. Consider that they are real people, take their loyalty rating into account, and then consider what they would know, and what the character needs to do to get them talking.
As for avoiding the technomancer doing all the digging with sprites and hacking, there are two considerations: risk and accessibility. On the risk side, it might be safer to promise your Lone Star desk jockey a beer in return for finding the owner of a car, rather than trying to hack the Lone Star database. Likewise with a lot of situations, where you have an insider. On the accessibility side, the information might not be on the net, or at least not in a place where the technomancer knows to find it. Lots of gangland activity is going to be word of mouth. Corporations might keep the guard schedule in a system without contact to the net, meaning that your corporate contact is the way to get it. And of course, all the swag, networking and favors can't be performed by the technomancer's sprites.