You chose 20 points. This is correct. You added to the 16 points we had calculated before, 1 point for a doubleton and 3 points for a singleton.
When you have added your newly calculated 20 points to the minimum number of points you think your partner could have which is 6, you get a total of 26. This total should help you to decide how high to go when you continue with your bidding.
In order to decide how high to bid, you need to know about scoring.
The objective in Bridge is for one partnership to score 100 points (GAME) on two occasions, before the opposition can do so. You get points for correctly taking the number of tricks that you promised by your bid. But how much you score depends on how many tricks you take, and what the suit is. Just as the suits were ranked for bidding, they are also ranked for scoring. The two lower suits (Clubs and Diamonds - also called THE MINORS) count 20 points for each trick that you take above the original 6 that you must make. The two higher suits (Hearts and Spades, also called THE MAJORS) count 30 points for each trick that you take above the 6 required initial ones. NO TRUMP counts the most. You get 40 points for the 7th trick (the first 6 don't count, remember) and 30 for each subsequent trick that you bid and make.
Since your objective is to get 100 points, if you were trying to do that in the course of one hand of bridge, you would have to bid 5 Clubs or Diamonds (5 x 20 =100 points), 4 Hearts or Spades (4 x 30 = 120), or 3 No Trump (1 x 40 + 2 x30=100).
You do not have to try to make your 100 points in one go. If your hand and your partner's hand are not sufficiently strong, you would be very rash to bid above the 2 level. However, if you bid and made a part game - and then on the next hand, your opponents bid and made their whole 100 points, they would cut off the part score that you had made. But there will be further details on scoring later. The important thing at this stage is for the opening bidder to decide how high to bid on his second bid (REBID).
There is a sort of rough guide to say how many combined points within a partnership are needed to make a game, and this guide says that with 26 combined points, you should on most occasions be able to do so.
We have ascertained that between us, we have at least 26 points, although many of these points relate to distribution rather than to honours.
7. What should the opening bidder's rebid be?