Best way to connect to SAP system from JAVA

There are lots of possibilities but a lot depends upon on your exact requirement and needs.

One way is that you can go ahead and use Java Connector also known as JCo. JCo is a prevalent option to do similar requirements as of yours. It has a lot of support available online as well.

Also, as you said Web service is by default the web standard and can be opted too. SAP functions are readily available and can be tuned effortlessly to be available as web services.