The headset is the set of bearings that’s attached to the frame’s head tube so that the fork can turn smoothly. It’s a very important component of the bike. Most modern road bikes use “integrated headset” bearings, which is not to be confused with the “semi-integrated” variety. If you don’t know the difference yet, make sure you ask your vendor. Semi-integrated headsets require you to press in a cup into the head tube before installing the bearings, but integrated headsets do not—that part is built into the frame itself. If your Chinese-made carbon frameset comes with the headset (and that’s becoming more common), the bearings are most likely made by Neco, or it may be a rebranded or unbranded headset which are made by Neco anyway. And if your frameset doesn’t include the headset, Neco headsets cost about $15-$20 USD on eBay. You can pay more for an FSA or Ritchey headset that has better (possibly more durable) bearings for $30-50, or a kick-ass one for more than $100. When you buy a headset, the one you should buy depends on the diameter(s) of the steerer tube. The picture on the right shows an example of the two standards of steerer tubes. The forks in the photo are for mountain bike which are different from road bikes, but the concept is the same. The one on the left has a wider (1½-in) base, and the one on the right is straight. So the one on the left requires a 1⅛” to 1½” headset, while the one on the right requires a 1⅛” headset. In both cases, the top of the steerer tubes are 1⅛” in diameter. Of course, all of your problems will go away if your frameset comes with the headset in the first place.
The stem, like your saddle, is a part of the bike that I do not recommend buying online unless you know exactly what length you are looking for. The reason is that you’re building a bike from parts that you have found online, and it’s difficult to know exactly how well it’ll fit you when it’s finally assembled. And fitting the bike is one very important process, during which saddle location as well the height and the length of the stem are finalized to give you maximum comfort and efficient pedalling. With the help of my wife, I do my own basic fitting at home. I would go to Mountain Equipment Co-op (one of the perks of living in Canada), buy three stems of different lengths. Once I figure out which stem fits me best, I refund the other two. If you do indeed buy online, an alloy stem cost $15-50 USD, Pay attention to the weight though, if it weights more than 200g, don’t buy it. A carbon stem costs $50-100 USD, depending on whether you’re buying a brand-name stem. They’re a bit lighter than alloy. Aside from the length, pay attention to the clamp sizes: you’ll need a 31.8mm “oversized” handlebar clamp, and a 1⅛” (28.6mm) clamp onto the steerer tube. (Yes, the mixing of imperial and metric standards is common in the bicycling industry, and can be daunting.)
Tip: Pay attention to make sure that the stem is actually carbon and not an alloy with a carbon surface.
Handlebar can be 40cm, 42cm, or 44cm in width. Generally speaking, the handlebar width is about the same as your shoulder. On pre-assembled bikes, the larger your bike (i.e. the large the rider), the wider the handlebar would be. Rule of thumb:
5’5″ or less tall → 40cm
average height → 42cm
over 6′ tall → 44cm
On eBay, carbon handlebars can cost between $60-$100 USD, and their weight can vary wildly, with the lighter ones weighing less than 130g, and the heavier ones close to 300g, which is no lighter than an alloy bar. There are considerable options out there, including handlebars that are integrated with the stem. I don’t recommend those because you cannot change the length of the stem which I talked about above. The option that you should consider is the geometry of the handlebar. The most popular geometry at the moment is the “compact” geometry (right side), which has a flat top portion that blends in with the brake lever. It’s thought to give the most comfort when riding. That said, each company has many designs to suit riders’ own preferences. The bottom figure has some of Cinelli’s handlebar geometries. There is also considerable debate even among professional cyclists over whether carbon handlebars are actually better than the slightly less expensive alloy counterparts, which can be as cheap as $20-60 USD. If you really want to know everything about the handlebar that you’re buying, ask the vendor about the handlebar’s reach and drop dimensions.
Handlebar Tape: A relatively cheap part of the bike, a pair of cork-type handlebar tape on eBay can be as cheap as $3 USD including shipping, plus 1 to 2 weeks for shipment to arrive, and that’s where you’re going to find the cheapest deals. I’ve been using the cheap bar tape like that for years without any complains, but there are definitely nicer—albeit more expensive—alternatives around. You can easily spend more than $30 for something more durable, and with better grip and feel, or with different patterns etc. But if you’re planning to spend more money on handlebar tape, you may want to consider going to your LBS first to see the options first hand before committing to buying online.