I don't have a lot of experience with it yet, but Loki looks promising for small projects. You'd still use it as a centralized logging server, but it's not as resource-expensive as something like self-hosting ELK.
I've only been using it for my homelab, and haven't even moved everything to it yet - but I like it so far. I already use Grafana+influxdb for metrics so having logs in the same interface is nice.