For a newborn with a long term investment horizon equity funds are best. You should consider fund costs in deciding between equity funds. Index funds, because they are passive investment vehicles often have the lowest costs. Most major fund companies offer some sort of S&P 500 index fund which would be suitable for a newborn.
I would suggest equity growth funds - given that she won't access them for at least 18 years they will most likely outperform fixed income or dividend funds. It would be wise to diversify between US and International equities.
Generally, this depends on when you want to cash it out and your risk tolerance. Look at funds managed toward a target year (e. g. expected year of college entry).
Small and Midsize company funds, Large Growth Company Funds,Large Under Valued Company Funds, International Funds,Specialised Funds and Bond Funds are the best mutual funds to purchase for a newborn baby.