I've found the assortment packs from Rockler to be very good quality screws, and actually to be cheaper than buying the individual 100- packs.
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"Square-X" screws will drive with either a phillips (everyone has one) or a square drive (works much better) bit. This combo pack is only available online. Rockler are the only tapered head wood screws I use now - don't bother with wood screws from Home Depot - they're awful. One time I thought I'd save time by getting screws there, and I twisted several heads off #10 screws. Waste of time and money. And I haven't tried them, but McFeeley's wood screws are supposed to be top of the line. They have combo packs also.
As far as countersinking, I have two suggestions: First, the Dewalt tapered countersink bits (DW2567, DW2568) are the best ones I've tried (better than Fuller or off-brands). These are available at Amazon and my local TrueValue. Sometimes they go on sale at Amazon for about $6.
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If you want a separate countersink bit, which is sometimes handy, I've found this type by Lee Valley to work very well. Easy to use, cuts cleanly.
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just got one of these a couple weeks ago, and it's already earned a permanent spot within easy reach by my bench. The Weldon brand version of these countersinks is supposed to be top notch.
Hope this helps, Andy