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I have a member managed LLC with three members. I am the managing member. I am buying a investment property cash. Should I buy in my name or the LLC? Also if purchased in my name, would it be wise to warranty deed it to LLC.

Are you buying it with your partners or is this an independent purchase?
If you have an LLC, I would say purchase the property in it (as long as it is a purchase that is split with the rest of the partners). If the property is just yours, purchase it in your name or in a different LLC. Don't mix independent purchases with partnership purchases in the same LLC. Not only will it drive your accountant crazy at tax time, but it may cause much confusion and paperwork.
Also, there are some states that recognize a Series LLC, where each property can be deeded into a different series under that LLC -- kind of like legs on a spider. If someone files a lawsuit because they slipped and fell, they can only go after that one leg instead of your entire portfolio in the parent LLC. I have also seen instances where there is a parent LLC and each of the Series under it can be owned by different partners (I have not done this, and am unclear of exactly how this works). However, I advise you to do some research and seek legal advice if you are interested in something like this. What works for one person in a situation might not work for all.
Good luck!