Sounds like a great idea to me. Go for it!
I built my business on word of mouth and only now, six+ years later, am I starting to get into more systematized digital marketing and other more expensive marketing strategies. I highly recommend staring a business page on facebook (it's free) and cross posting with your own personal page (free). Also, the realtors and property managers are a great idea. They are the ones most likely to talk with the family and, as part of their service, solve the problem of baby equipment (and land their rental) by calling you (win-win). So, go find them at chambers of commerce, networking events or, even calling them out of the blue and going to coffee. At the beginning, this is more time intensive BUT it is free. Keep the costs low, become cash flow positive and then grow.
If you can take calls, return calls, be responsive, listen, eat bad contracts, invoice/f/u for payments, be nice - you'll be shocked how fast the word spreads if there is a market. It sounds like you know there is a market - seize it!
On the liability insurance - call your insurance agent and get a cheap general liability policy and then forget about it. I'm actually a personal injury attorney who sues people. I can tell you - we want to get to insurance policies. I have no interest in taking people's personal assets. I know other PI attorneys who have been in the biz for decades, are the best at what they do and they actively discourage lawsuits against people in their personal capacity. We want insurance money, plain and simple. So, get a general insurance policy and rest easy.
On the rental contact, do your best with the first draft. It won't cover everything. Also, I've found that these types of documents really aren't very valuable. I follow the golden rule - customer is always right. Someone breaks our stuff? Feel them out, see if they are a good person who recognizes they messed up, send them a fair invoice, see if they pay it. If they don't? Do not get in a pissing contest over a few dollars. I see attorneys put their former clients in collections over an unpaid bill and I think they are so dumb. Cutting of their nose to spite their face. If I have a unpaid accounts receivable that I know I'm not going to get and I make a phone call to the client, who is now avoiding me or embarrassed by the balance, and I say, "Tough times right now, huh? Well, let me help, I'll waive your outstanding balance but I want something in return. I want you to go around town and talk about how I'm the best and nicest attorney you know. I want you to write me a good Facebook review and I want you to actively look to get me a referral. If you do that I'll be able to make up for the money I'm losing by writing this off. Can you do that?"
I've never had someone refuse that offer. Consider the difference in attitude compared to suing someone. Dumb, dumb dumb.
Also, set up payment systems where you do not accumulate a large accounts receivable. 50% down and payment upon delivery or something like that. I only get in arrears on "special" cases. So it's not like I write off huge sums of money - but it happens sometimes. For you it will happen with damage to your rental. Don't fight, turn it to your advantage.
Anyway, if you have liability insurance and you know you are not going to get in a pissing match with your clients then your problems are solved. Go forth and be profitable.