Well your best bet is Blender. As you will be wanting to render the model etc. Blender is free and has a quite remarkable list of feature for the low low price of:
£NOTHING
But it does have a massive learning curve. If you get over it, it will probably be well worth your time invested in learning it if you have great need for things like renders and game models.
Thats if you want an animated logo btw.
If you want a still logo just download GIMP. Its like photoshop, without the price tag and fewer features.
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