I would like to use the Mylyn task-centered user interface however i regularly work between two pcs and would rather not purchase any bug tracking software.
Can someone please recommend a good connector to use with Mylyn for my situation or some other workflow that is better suited.
Cheers.
The best Mylyn connectors for free trackers are the bundled connectors for Bugzilla and Trac. So one option would be to find a hosting site that offers Trac, e.g. Assembla, which offers free hosting for open source projects and moderately priced closed projects (I'm quite happy with them, Trac, and Mylyn). Be sure to set up the connection using XML-RPC if you use Trac, else you won't get the rich Mylyn editor.
I can recommend you to use Foglyn connector together with FogBugz server. FogBugz server is free for 1 or 2 users, and you can also get free Foglyn license for this edition of FogBugz. Furthermore, with free FogBugz you also get Kiln, which is Mercurial-based Version Control and Code Review system, although you probably won't use its code review part. You can use free FogBugz + Kiln for any number of projects, open source or not, the only condition is number of users (max 2). Big advantage is that you don't have to run your own FogBugz server, but you can use hosted solution. This makes configuration very easy.
(Disclaimer: I'm author of Foglyn connector)