I'm not an accountant, so what follows is not accounting advice. For that, you need an accountant. However . . .
The advice below is correct. Many lenders won't lend to an LLC under any circumstances. Those that will want the LLC to be well-established or else they're going to want you to personally guarantee it.
Rather than jumping through all those hoops, you may just want to buy it in your own name, then immediately transfer it into an LLC. The mortgage will be in your name (so your exposure would be the same as if you personally guaranteed it).
Check with an accountant but, no, there aren't tax benefits to owning it in an LLC versus your own name. The profits and/or losses in an LLC will flow through to your personal return in any case.
The advantage of having the property in an LLC is that it provides a measure of asset protection. Not perfect, but--if done properly--moderate. So if, let's say, you personally get sued for something, you may be able to protect your investment property. Check with an accountant or lawyer, but what you want is a multi-owner LLC, not a single owner LLC. Similarly, if a tenant trips and falls in the rental property, a properly constructed LLC may isolate the tenant's recourse to the LLC and not allow him/her to touch your other assets.
An LLC sometimes is also useful for transferring ownership. For example, there are times when you might want to transfer ownership by selling the LLC that owns the property, rather than actually selling the property. Some investors do that when buying foreclosures. They don't intend to hold them for long, but they'll buy them in the name of the LLC, then sell the LLC.
A land trust actually provides more protection than an LLC and accomplishes the same things. See http://www.landtrust.net
Again, check with a lawyer and accountant as appropriate.
Hope that helps.