I think the most critical factor that you should consider is your target audience.  The question mentions a "specific product."  Who is that product aimed at?  Kids? Women? Men? Adults?  Once your target audience is known, then you should tailor your media choices toward being able to reach that target group.  For example, if your target group is stay-at-home moms or dads, then television or radio advertising during the middle of the day might be most effective.  If your target product user is an athletic, outdoor sports enthusiast, then magazines, web advertising, or later night television might be most beneficial.  

The second factor that I believe is critical to your media plan is cost.  Television time is expensive, but it does reach a wide market.  Magazine advertising might be more cost effective, but it does assume that your target audience is financially able to purchase the subscription and motivated enough to keep reading the magazine month after month.  You could even decide to use your entire budget on a commercial that will air once . . . during the Super Bowl.  Regardless of your final choice, a cost vs. benefit analysis will need to be done in order to determine whether or not a particular medium is worth the money being spent on it. 

The main factor that you need to consider is the target group or groups that you want to influence and the types of media they are most likely to consume.  

For example, if you are trying to target an upscale audience, print might be a consideration.  People with a lot of money might be reached through things like travel magazines or golf magazines that deal with the sorts of interests that appeal to the wealthy.  By contrast, if you are trying to reach people who are more down market, you might consider commercials on daytime or late night television.  

In other words, you have to know your target market and the types of media that are most likely to reach them.