Probably one of the better books on the topic is around $30, Two Knotty Boys' Showing You the Ropes . If you want cheaper, The Little Guide to Getting Tied Up seems to have good review scores and is closer to your budget, though I can't vouch for it myself, not having read it. I haven't read Learning the Ropes either, but judging by the description, it doesn't appear to be a manual for rope bondage, but rather an overall guide to BDSM.
If that's what you're looking for, I can point you to a few recommendations. Probably the most celebrated book on general BDSM (at least among those I've spoken to) is Screw the Roses, Send Me the Thorns . Also, while it's more about polyamory than BDSM, The Ethical Slut is a highly acclaimed book about a sex-positive lifestyle.
I would caution, however: be careful with being pushy about BDSM and sex-positive stuff if you're not sure the person will be receptive. Yeah, I get that it's a "gag gift", but you want to be sure you're not insulting your cousin or making things awkward between you.
In any case, I hope whatever you go with works well for you!
No one is going to know the two of you better than the two of you. While it can be fun to swap techniques with other players, most "mentorship" relationships are unnecessary and often smoke-screen for toxic dynamics.
My favorite book in my library to loan to the recently-interested is "Screw the Roses, Send me the Thorns ." It's certainly "classic" and legend has it that it was orginially laid out on a copy machine, but it remains one of the best survey-level resources out there for loving people doing this stuff because its fun in a non-commercial setting. Revolutionary for the time when most media was centered around Commercial Domination(tm.) A classic then, still excellent now.
I have so many "technique" books it's hard to narrow them down, but the first I would pick up is "Jay Wiseman's Erotic Bondage Handbook ." Rope is useful, rope is cheap, rope is versatile, and with a few simple guidelines rope is remarkably safe. The biggest guideline being "don't do weight-bearing rope unless that's a specific fetish you're into and have spent a few years getting good at it." This book isn't about Japanese-style rope with an eye towards moving on to suspension, although I have books like that and I love them. This is about using Western style rope to keep things out of the way while having safe, sane, and consensual sexytimes. Simple techniques, creative applications, and a thrumming focus on safety make it a great start.
Comboing the two should give you a pretty good start on some neat ideas, save you some dosh by making it easier to put together a toybag that's not going to require a lot of cash outlay, and hopefully keep you away from handcuffs. I own a pair, I use them for capture play, but the can be prone to causing injuries both superficial and serious so you really don't want to be moving around while wearing them. Rope may not be 100% safe but it's certainly safe-er.
If you're interested in branching out a bit more, or you learn better from videos, or you would like to get your education and your porn fix at the same time, kink.com's Kink University has both a commercial site and a free sample feed of guest teachers that cover a wide, wide variety of activities with a focus on learning enough skills to have fun while getting an overview of what the kink/activity "is."
If you don't mind being marketed to a bit, Extreme Restraint's XR University and their Pornhub mirror, which is not verified so I won't link it here, are also excellent. Generally the two hosts bring in a guest star and speak to them about a certain kink for the first half of the vid, then do a hands on demonstration for the second half, interspersed with two-three commercials. The good news is that they go very in depth on the products used, make recommendations for ones they particularly like, and make it clear where they can be purchased. The maybe-bad news is that's because they sell them through their online store and are doing this to make money. Personally, I respect the hustle, love the videos, and think selling toys by teaching people to play with them is a great idea where everyone wins, but I don't judge the people who are bothered by the idea it's primarily an infomercial. Your mileage may vary.
In short, don't spend money on dominatrix time unless you just want to spend money on having that kind of experience. Do talk with each other and if you feel like it grab a few books and some pleasant-enough-feeling cheap rope and experiment. You can, and almost certainly will, buy more expensive and specialized stuff later, or just learn some techniques for safely manhandling each other that make rope unneeded if you get into that. Or all of the above. Mostly, just have fun and take care of each other and everything else will work out. Good luck and have fun.
(Disclaimer: links to commercial products and websites included for convenience only. I have no business relationship with anyone in this post other than happy customer and receive no compensation other than the warm fuzzy feeling of passing on recommendations that were given to me when I was starting. 1/4 inch nylon is fine and if you tie it in a pillowcase you can just chuck it straight into the washing machine and dryer. Fnord.)
Try this book .
or DL the pdf.
It is pretty much my go-to beginers guide to the scene. This is how my first kinkfriend got me into it, and I have been a fan ever since!
Also, go slow, small steps, and do only what is fun for you both. And, yes, communication is key.