The fastest speeds for the respective media, as far as I know are:
So when you say no slower than 4x, you are in fact asking for the top speed, and your price range may be a little optimistic.
click here for an idea of the range of products available.
If you've decided on the DVD minus platform, there are a few models close to your price range - Asus and Pioneer.
I'm a little surprised that the DVD minus writers are not cheaper. You may be able to get cheaper ones somewhere else.
Personally I would opt for the DVD plus platform, or at least hedge one's bets and choose a rewriter which can write media from both platforms, such as the Sony DRU500A.
NEC is releasing an ND-1300 in May which is pretty close to your price range, and writes both DVD plus and minus media.
NEC also makes pretty cheap DVD plus writers and is not a bad choice.
Note that the cheaper models come with little included software. It works well if you already have software which can record DVDs, but if you don't, you have to factor in the price of additional software which you may have to purchase. That is why the Sony dual platform writer is actually quite reasonably priced.