I have built a java web crawler/spider before with a front end resembling google for a previous uni project and I would say it is a moderate program to try and do, not overly difficult but a definate challenge for a new java coder.
Some of the main bits you will need to learn to do this is iostreams to read the urls in and JDBC so that you can store the data(you could do it by reading into an array/vector but i wouldnt recommend it as it would eat memory).
There is loads on the web about spider methods and algorithms like word ranking etc but i am sure you have already read up about how they work.
It is probobly quite a good project as you could make it on the command line and then redo it with a gui later if you wanted to.
As for browser plugins I would probobly go for a firefox plugin but then again why stop at a search engine, why not build your own browser too. :mrgreen: