Same exact tax benefits with or without an LLC, as long as you're the only owner.

Real estate investors are attracted to medium-term rentals to gain the benefits of extra cash flow versus long-term rentals while avoiding regulatory risks, high turnover, and intensive management of short-term rentals.While many investors are now turning to medium-term rentals to build their portfolios, the lending world has unfortunately been a little slow to keep up.

Can I still claim the tax benefits for this property under my LLC? 

Agreed, I don't see much benefit in lender financing if it's going to cost me more.

You can usually also benefit more by simply using the seller or builder credit to do a simple "Rate buydown".The first rate on the buydown is a "teaser" rate that only last for a short time 1 year for example but a true rate buy down is for the entire term. 

One big benefit is that these loans look at the property’s income rather than the borrower’s personal income, which can make qualifying easier for investors with multiple properties.

I figured there might be some benefit on interest rates for the 25% or 30% down. 

Chicago has solid cash flow markets and many appreciating markets with much lower cash flow.Interest rates are significantly hurting cash flow, so in my opinion, this is a time where you have to settle for low cash flow, knowing that there are also tax benefits, debt pay down, and appreciation happening.  

There is now essentially no benefit to obtaining a second home loan over an investment property loan, except for the ability to do 10% down rather than 15% (minimum for investment properties).This info is all related to Conventional mortgage financing.

Consider Future ScalabilityA fourplex is a great starter deal because it combines the benefits of multi-family while still qualifying for residential financing.