The social media campaign
This all depends on the overall goal of the campaign and if you are able to reach it. What do they want to achieve? Canva will be fine for your needs. The cost to entry for Facebook can be pretty low. Look into the video if that's a possibility. I've recently had some great success running video view ads.
I use
Canva, but it's only workable if you have assets from the business you're advertising for. The cost of running the campaign should be what they get for free, not FB's ad fees - ask for a budget, be prepared to show spend, though.
"How much is optimal?" There is literally no answer to this question. More than $5 per day or whatever the minimum spend is in your nation. If you have to pay for it yourself, what is a testimonial worth to you?
More importantly... what is this whole deal about? You're offering to perform work that you don't know how to do, for free, in order to be recommended to continue doing so? This is the most ass-up strategy I've seen for anything.
"What would you offer to ensure a great testimonial and case study?" I'd offer some services that I actually feel confident in performing. Also, it's hard to force a case study - if you're doing something just for the sake of a blog article, make it up!
Yes, it is a horrible strategy. Setting out in business to do something you have literally no experience in doing is a horrible strategy. Sorry, but facing cold hard truths is step 1 of getting anywhere in business.
Why not run the campaign for your own brand? Experiment using your own social media accounts first - this is something I did when I started out in freelancing. Rather than setting yourself up to fail, which is exactly what you're doing, try working out some kinks in what you're doing before putting yourself in front of a client.
Just out of curiosity, how old are you and what industry are you in? Social Media Marketing, done correctly, isn't something you can just pick up and run with. There are thousands of stay-at-home moms and crackpot fools who call themselves "social media gurus" and have never opened Power Editor or formed any idea of multi-channel ROI. Reading a few books and blogs is likely to expose you to more bullshit than actual useful advice. An easy 90% of what I read is just blatantly incorrect.