What are some good introductory rules to bridge?
Rubber and Contract bridge aren't two different types. Rubber bridge is a form of Contract bridge. 

There are essentially two forms of contract bridge these days


Duplicate Bridge
Rubber Bridge


In both forms (i.e. contract), for one deal, there is a 52 card deck dealt, the players do the bidding to determine the level and trump (or no trump), and depending of whether they are declaring or defending, they either try to make or break the contract.

The differences come in the mechanics around a set of deals, and how the deals are scored.

Rubber is mainly geared towards four players playing for money, and most of its quirks might have been derived from whist.

Duplicate is the form of bridge more prevalent these days and tournaments are held using that.

The raw scoring for a particular deal is almost the same in both rubber and duplicate: Declaring side makes 20 points for clubs/diamonds (i.e. if they chose clubs/diamonds as trump), 30 for hearts/spades (if trumps). 40 for the first no trump, and 30 for the rest.
Defending side gets 50 or 100 points for each undertrick. They get a 100 if the declaring side is vulnerable, which is determined differently between rubber and duplicate. The contract could get doubled and redoubled which might affect the score, but I suggest you ignore that for now.

100 points makes a game, and in order to get the game bonus you need to bid to the appropriate level and make it. Similarly you have the small slam and grand slam bonuses.

The difference between the raw scoring for Rubber and Duplicate comes in the bonuses calculation I believe (part score bonus, redoubled overtricks etc). I suggest you don't worry too much about those differences for now, and just remember the 20/30/40 and 100 for game.

In duplicate this raw gets converted to a different score, depending on the kind of duplicate. 

In rubber, the raw scores get added up in various ways, in addition to rubber specific bonuses, and if you are playing for money, gets converted to money! :-)

For a beginner, I would suggest you forget about the scoring (apart from what was said above) and concentrate on the play first, and then the bidding, for a single deal.

The 30 making game scoring is probably an ancient form of bridge called auction bridge. I suggest you ignore that (and please check the publication dates of the books you read).

Hope this helped clarify some.