Vanguard Admiral shares typically require a minimum investment of $10,000, whereas the Investor shares typically require $3,000. For the lower expense ratio funds, the former have expense ratios of around 0.04%--0.07% and the latter have expense ratios around 0.14%--0.19%.
If one were to invest $10,000, would it be better to opt for Admiral shares in a single fund or Investor shares in three funds so as to diversify with regard to cap size and growth/value?
If I were in your shoes I'd probably take the Vanguard Total Market fund with Admiral shares, then worry about further diversification when there is more in the account.
Many times when you "diversify" in to multiple funds you end up with a lot of specific security overlap. A lot of the big S&P 500 constituents will be in all of them, etc. So while the 10 or so basis points difference in expense ratio doesn't seem like enough of a reason NOT to spread in to multiple funds, once you split up the money between Large, Mid, Small cap funds and Growth, Value, Dividend funds you'll probably have a collection of holdings that looks substantially similar to a total market fund anyway.
Unless you're looking for international or some specific industry segment exposure and all of the money is going to equities anyway, an inexpensive total market fund makes a lot of sense.
There's really no right or wrong answer here because you'll be fine either way. If you've investing amounts in the low 5 figures you're likely just getting started, and if your asset allocation is not optimal it's not that big a deal because you have a long time horizon to adjust it, and the expense ratio differences here won't add up to that much.
A third option is Vanguard ETFs, which have the expense ratio of Admiral Shares but have lower minimums (i.e. the cost of a single share, typically on the order of $100). However, they are a bit more advanced than mutual funds in that they trade on the market and require you to place orders rather than just specifying the amount you want to buy. A downside here is you might end up with a small amount of cash that you can't invest, since you can initially only buy whole numbers of ETFs shares. So what I'd recommend is buying roughly the correct number of ETFs shares you want except for your largest allocation, then use the rest of your cash on Admiral Shares of that (if possible). For example, let's say you have $15k to invest and you want to be 2/3 U.S. stock, 1/6 international stock, and 1/6 U.S. bond. I would buy as many shares of VXUS (international stock ETF) and BND (U.S. bond ETF) as you can get for $2500 each, then whatever is left over (~$10k) put into VTSAX (U.S. stock Admiral Shares mutual fund).
In general, I'd try to keep things as simple as possible. If your plan is to have a three-fund portfolio (like Total Market, Total International, and Bond), and keep those three funds in general, then having it separated now and adding them all as you invest more is fine. (And upgrade to Admiral Shares once you hit the threshold for it.) Likewise, just putting it all into Total Market as suggested in another answer, or into something like a Target Retirement fund, is just fine too for that amount.
While I'm all in favor of as low expense ratios as possible, and it's the kind of question I might have worried about myself not that long ago, look at the actual dollar amount here. You're comparing 0.04% to 0.14% on $10,000. That 0.1% difference is $10 per year. Any amount of market fluctuation, or buying on an "up" day or selling on a "down" day, is going to pretty much dwarf that amount. By the time that difference in expense ratios actually amounts to something that's worth worrying about, you should have enough to get Admiral Shares in all or at least most of your funds. In the long run, the amount you manage to invest and your asset allocation is worth much much more than a 0.1% expense ratio difference. (Now, if you're going to talk about some crazy investment with a 2% expense ratio or something, that's another story, but it's hard to go wrong at Vanguard in that respect.)
