op - I found some fun "10 min maths" challenge books for similarly inclined DS - or there are some fun apps around nowadays. Maths keeness should definitely be encouraged, IMO, but tables are not the most interesting option (although clearly there is no reason not to do that too, if he wants to)
I would teach 2,5,10,3,4,6,8,9,7 - although 9 has a nice pattern so lots learn it early on along with the 11. In our school we aim for every child to know their 1-10 times tables by the end of Year 4 so we do countig in 2,5 and 10 is year 1. Knowig your 2,5,10 times tables in and out of order in Year 2. 3,4,6 times tables in Year 3 and the rest in Year 4. Although my last year 2 class left knowing their 2,5,10,3,4 and 6's by heart (I teach the higher set of children), because like you DS they are keen to learn them.
If he likes them he may want to learn them in order (2s and 10s probably easiest though to start with though). I do think if children like maths they often like order. Certainly make sure he understands division (sharing!).
We do 10, 2, 5, 4 (double 2 if he loves patterns then this one is easy), 3
From then on you can pretty much choose. if he liked 4s and saw the 'double twice' pattern easily, then 8s are the obvious next step. Or you can do 6s, which are double 3. Or 9s because they have a fun pattern and many children find them easy to learn. 7s are probably the hardest but if he knows all the rest then only 7x7 to learn by then.
My DS knew 10, 5, 2, 11 and 9 in Reception because he loved the patterns. The only others he actually 'learned' were 3 and some of 7, the rest he quickly derived from what he already knew.