James,
With regard to selecting a name, it is a good and very important issue - Ipsi's comments I think are right on. I will add my own additional comments below.
1) If you are in school or at work, ask your colleagues for some recommended names. Start creating a list, maybe get like 10 or 20 names. Once you get a list together, then ask another non-related group of trusted people which they think is best.
I would go with something really standard - common last name, 3 characters in total.
2) I would try to find a name that phonetically is related to my own, but it is not real important should you not find a good phonetic fit. Phonetic consideration should be part of the first round to see if some cool name would sound like your own. But if not, its not a big deal (mine is fully dreamed up, nothing to do with how my English name sounds and has served me well), so do not keep to the phonetic route at the expense of a good Chinese name.
Having a name that is reasonably normal is REALLY useful when in China living life. (e.g., like telling the laundry people what your name is for a ticket. I saved my name in my phone and could show people by bringing up my address book. Now, I can write it or tell them and get the point across most of the time.
Having a good standard name becomes even more important and the Hospital or the Bank.
Bank of China tried to use my English Name and they could not make any sense of it (I did not have my Chinese name with me at the time and could not remember it). I filled out papers for a checking account, savings account, a bank card, phone banking, and internet banking. In the end, their computer system could not accept my name for internet banking because it was too long. So I had to sign 5 more pieces of paper to reverse the initial account setups, and then they had to hodgepodge my name so some shortened English version. Then 5 more pieces of signed slips to get the account that way. So I left that day with 15 slips of papers. I believe they would have taken my Chinese name of 3 characters, and I might have left with only 5 papers.
The Hospital definitely took my Chinese name and ran with it easily. They had my passport info and all, but all filing is under my Chinese name. I did not have any major problem, but they addressed issues with a hurt foot, back, etc. If I go back, I just tell them my name and they pull the file.
For places like hotels, hospitals, etc., (just about everyplace but airlines) they likely want to see passports and names, but they want to enter a Chinese name into their reference system, so having a normal Chinese name again provides benefit.
As for finding my own Chinese name, I had a party at my flat with some coworkers. The party was not for my name, but kinda wound up being that way. They knocked it around for a good hour, and came up with mine.