Definitely implement OpenTelemetry [0] instead of specific providers sdk even if promised to have better features. Lock-in is hard to escape when you need ship 2 features for yesterday. However OTel is quite young though (still not GA) so you'll feel some missing features (logs are still WIP for ex).
On the question of where to host the data, on the early days i would recommend to opt (if available) for your cloud platform products (Stackdriver for GCP for ex) since it will be easier to setup. Later on you will be able to easily switch to something better as your needs will evolve.