Keep it as simple as possible.
Lambdas and all the serverless stuff is great until it isn't anymore, because you need another service for this and another service for that which gets a) complex quickly and b) expensive, too.
For an MVP, go EC2 or ECS and a database, possibly S3 storage depending on what you need. MVPs are all about learning about the problem in the most cost-efficient way possible
"AWS backend" can mean sooo many things - you will get better answers if you describe your architecture in a little more detail.
Costs, blindly following their reference architectures will get you lambdas everywhere and microsservices everywhere and other upsells that will cost you a lot. Also, do not use their WAF/CDN, again, costs.