Which's the best mutual fund for IRA to start with?

I have around thirty years horizon.

Without knowing all your info (risk tolerance, income, etc.), it is hard to say, but all other things being equal, I would say something like Russell 2000 Index Fund or a managed fund that is designed to change based on your time horizon like a Fidelity Freedom Fund.

I don't know what 30 years horizon is, but your IRA would depend on your age, your investment style and how much money you have to play with.

In general it is best to stick with an index fund (such as an S&P 500 fund), as these have very low costs and usually perform close to market. Going to a managed fund may yield decent results in the short term, but it is likely to underperform due to high management fees. Vanguard offers the cheapest cost index funds. This philosophy has been said by numerous investment legends including John Bogle, Ben Graham, and even Warren Buffet.

Since you have such a long time horizon, it would probably be best for you to invest predominantly in equities and minimally in fixed income or bond assets. The key will be to stick to the equities and not knee jerk everytime the market turns down.

There are lots of good funds out there - and even more bad ones.

If you are unsure, start with Vanguard SP500 fund (VFINX). It's got low overhead, and will at least get you (almost) the same return as the general market does.