Things to bring here:
Clothes. It's not very cold here in the Winter, never goes below 0 degree. You don't need a very thick coat in Winter. A 薄防寒服 (大概有夹层绵或者什么的就可以) will work. Summer is relatively long here, almost from mid May to the end of September. You would like to have a lot of T-shirts. Summer is pretty hot in the daytime, but usually cools down at night, so you can usually get good sleep. :) I usually do laundry once a week, and in the Summer time, that means, at least enough clothes to last for 1.5 weeks. As for the coat for the Spring, Fall, you just need 2 to 3 (it is not necessary to change your coat every day). Again, these are all my personally understandings. Actually, the more, the better. If you are a girl, you will find that it could be hard to find clothing of your size when you just come (I mean, you don't have a car to go to fancy shopping centers). My recommendation on clothing: try to make them comfortable. Most of the chance you will bike when you just come here, you want to dress comfortable when you bike. And people don't usually wear formal dress to lab and to classes.
锅碗瓢盆。 锅一般不用带，旧货店买起来挺方便。可以考虑带一个小高压锅，这里的高压锅和国内的不一样。别的锅如果你有地方想带的话，一定带平底的，圆底的锅这里很不好用。 碗可以带一两个(够你刚来时用就可以了)，也可以不带。如果你喜欢做饭，考虑带合手的菜刀过来，一把合手的刀可不易得。刀板一定不用带，公寓里都配有的。 调料一般不用带，这里的中国店(其实不在Davis,在Sacramento)东西挺全，酱醋都还正宗。不过如果你喜欢吃辣(象我一样 ：)的话，考虑带些辣椒过来。这里的辣椒可不够辣。 对了，有人问过我花椒、干椒等飞机上可不可以带，答案是可以的。不能带的是新鲜蔬菜水果，因为那些可能携带病毒。干料、腌制品等却是可以带的。
Software. The more, the better. You will find getting the software you want is much much harder here. Also, if you want to take your own files here (like addresses, etc.), be sure to change the file names to English. The English Windows often does not recognize the file name in Chinese. I ran into that problem when I just came here. It would be fine if you have Chinese in your text. You will learn the way to read and write Chinese on English Windows after you come here.
Others. As far as I can think of, I would recommend a small flash light (手电筒), a chain lock for bikes, and a raincoat for biking. A flash light is required, not only recommended by law when you bike at night here. A small one with 2 AA batteries will work perfectly. It rains a lot in the Winter, and the raincoats here are not as good as we have in China for biking.
Gifts. I don't think you need to bring gifts for your lab mates or class mate upon your coming. If you like, you can by some small stuff (like bracelace, 剪纸，脸谱，bookmarks ... ), to give to your friends at proper occasions later.
Money. $2,500 is recommended, to be safer. Mainly because you might need to rent an apartment yourself, ~$1,500 will usually be needed for the deposit. However, if you find a permanent housing before you come, then you don't need that much. Usually you will not get your first salary for the first month, and you money to live through that month (or, could be longer).