Different people have different risk aversion. So you need to find an allocation that works for you.
Standard advice is to go read something like
https://www.bogleheads.org/wiki/Asset_allocation first.
When one talks about "life emergencies" there are broadly speaking 2 categories:
major life emergency: high amount needed, very low probability of happening. eg: unexpected, expensive heart surgery
minor/normal emergencies: small amounts needed, higher probability of happening. eg: car breaks down - need down payment for new (economical) car. lost job - need 6 months living expenses.
Here's how a hypothetical person (eg: me) could go about it: I could decide the following allocation suits my risk tolerances: 80% US total market index (VTI) 20% bond index (BND).
I would make sure all my bonds are in my tax deferred accounts. Then in taxable accounts:
Choose to keep the minor emergency fund in a savings account (eg: 3-6 months living expenses)
Invest the rest in VTI . My "high amount needed but low probability its needed" emergency fund would also be invested here.
Any of the funds listed here would suit the job for the second type:
https://www.feex.com/funds/Equity-US/VTI I went through a phase of following more complicated DIY asset allocation using futureadvisor.com and hence am stuck with capital gains. But if I had to do it all over again, I would just go with 60% VTSAX (or VTI), 30% VFWAX/VEU, 10%VBTLX/BND across my total net worth (other than my minor emergencies fund) and be done with it except for rebalancing once a year.