Windows Communication Foundation can be used to create both SOAP services (great if your consumers are businesses, using Visual Studio/.NET or Java) or REST services (for people on other platforms). Those are the preferred means of exposing public APIs.
If you want maximum exposure, probably best to use the REST approach, since it is easier to consume from "web" languages like JavaScript. Microsoft has extensive resources on putting together a REST API using WCF.
Honestly, for the kinds of requests you say you need to handle, which all seem to be looking up data as opposed to modifying it, the difference is almost trivial - you can switch from SOAP to REST simply by changing a few attributes/configuration options and you could technically even host both at the same time using very little additional code. As long as you stick to WCF and don't use outdated technology like ASMX/WSE then you will be fine.
Reasons to use REST:
- Consumable from almost anywhere (including JavaScript, RSS readers, etc.);
- It's popular (in use by Google, Twitter, etc.)
- Supports many different data formats (JSON, Atom, etc.)
Reasons to use SOAP:
- Standardized security protocol (encryption, non-repudiation, etc.)
- Distributed transactions
- Message Queuing
That's not an exhaustive list but it should give you an idea of who the target markets are for each. If you're hosting a very open, very public site designed to be consumed by anyone and everyone, go with REST. If the service is part of a business system and you need to guarantee reliability, security, and consistency of data, you'll want to go with SOAP. Choose the appropriate technology based on your target market.