(This comment pertains to Vanguard funds cause I don't know Fidelity). For long term growth you'd likely want either all-stock or a balanced fund, with the lowest costs possible. Unfortunately, funds like Vanguard 500 Index Admiral Shares (cost ratio of 0.05%) have a min of $10k, and 500 Index Investor Shares (cost ratio of 0.16%) has a min of $3k.

So below $10k you're not going to get the best expense ratio, and many of Vanguard's funds have a min of $3k so you can't buy the Vanguard LifeStrategy class or 500 Index fund either. You CAN however buy a Vanguard Target Retirement fund ($1k min and ~0.12-0.16 expense ratio). You don't have to use it for retirement -- you can invest in it just like any other fund, and if you choose a longer horizon the fund will be 90/10 stock/bond or 80/20 stock/bond biased.

With 1k you should hold it in cash unless you have some ability to get shares through a special program (employer, trade organization, club, etc).

With 2500 you should go FSTMX.

(Don't take investment advice, including this, from strangers on the internet)