I'm a bit overwhelmed at financing options and timelines

[Tom Horn]

First time investor here. I'm looking to buy a long term rental property about 1.5 hours away from where I live. I'm wanting to buy this summer, so about 2 months from now, and I'm trying to explore my financing options now so that I can jump on a deal if/when I find one. I own my current home outright, which has a value of around $250k, and I have $25k cash saved up. Here are the options that have been presented to me.

1) Some lenders I'm talking to are trying to convince me of a HELOC, but I don't really like the variable interest rate. I don't like the idea of of take a roughly $125k loan on a variable interest rate.

2) I asked about a traditional/conventional loan, in which I put down the $25k of my own money, and then financed the remaining amount on a traditional mortgage. One lender tried to tell me that my interest rate would be higher by doing this, and that I should try option 3.

3) Some lenders are trying to convince me of a cash out refi / home equity loan (I'm still fuzzy on what the difference is between them). The benefit of this is that I would have the money in my account, and it would allow me to make a cash offer on a house. However, I don't like the potential scenario in which I take out the loan, start shopping for houses, and don't really find any good deals. Then, I have this $125k loan that I'm just paying for every month out of pocket.

I'm leaning towards option 3, but how can I do the timeline here? How long roughly does it take to close a home equity loan/cash out refi? Could I go "make a cash offer," then immediately run to my bank and secure the loan (because I will be preapproved)? What is the timeline on that?

Is there any other advice that yall have for me in how I approach this?