The reason I didn’t come straight out and ask them for a months worth of deposit to hold was because she told me they can’t move in February 1 because they have to give their landlord a 30 day notice plus pay him there earned rent money for February.

Your lease will most likely grant you access with a 24 hour notice; might as well get a head start on your construction plans, bring some contractors through for estimates etc - your tenant might decide to move sooner without you paying extra.

I have a slight broken gutter in the back so that may turn some people off (it's not hanging down just slightly broken and off by a few inches but definitely noticeable), it is an easy fix and I plan on having someone fix it this week.  

Small world.As I'm sure you've noticed, there's a ton of different ways to invest and tons of financing options.

Also, I am noticing that available rentals are staying empty for up to two months, which is unusual in Austin, TX. 

@Arlen Chou Good point, I noticed that in Texas. what do you suggest on low property tax state : FL, NV, AZ ?

We give the tenants 2 week notice and it is in our lease.

Having notice to reader financial statements.

I was not smart enough to put the dates together and notice that the place was not Winterized through that first Winter. 

You just have to give a notice to the tenants 6 months before the lease expires.