I don't understand exactly how fees work on funds. When do the fees get charged - when you buy shares of the fund? For example, say I buy $100 of shares in XYZ fund every paycheck. It has a 1% expense ratio. Does that mean I'm charged $1 each time I buy and actually only invest $99? Do you pay fees on gains if the fund value goes up?
If the fund has a front-end load (think Class A, B, C, etc... shares), then that amount is taken out when the shares are bought. I know my 401k doesn't have any funds like that, but they do exist, at least as options for Roth IRAs (Waddell & Reed is an example of a company which has funds with front-end loads). Run, don't walk, away from those!!!
The expense ratio (ER) is taken out of gains before they appear in your account, you never actually see the money coming out. For example, if the ER is 1%, and the fund gained 10%, the gain you would see is 9%. In general, the lower the better. Vanguard usually has very low ERs. Unfortunately, the ERs of 0.46% to 1.17% are pretty normal, I'd try to keep them as low as possible. What is the fund with the 0.04% expense ratio? I'd definitely try to invest in that one, as long as it's within your desired asset allocation.
The target fund allocation for the 403(b) splits my money between all 12 funds. Would it be wiser to research all of them and choose a couple in each category?
Yes. I think you said you're 35, right? A general rule of thumb is your age in bonds, (100-age) in stocks. So, you'd want about 35% bonds, 65% stocks. Another school of thought is, for goals that are 10 years or more away, 80% stocks, 20% bonds. It really depends on your personal risk tolerance.
For the percentage of your portfolio devoted to stocks (stock mutual funds), you want to diversify between large cap, small cap, and international. Are you contributing to an IRA (Roth or Traditional) at all? If so, those also count towards your desired asset allocation. If you google "Lazy Portfolio" you can dig up some example asset allocations and go from there. Good luck and congrats on paying off the car so quickly!!