- To select the squad for a series, who are involved in it?
- To select the playing 11 for a match, who are involved in it?
that is, who has the most rights to do it?
Selecting squad for a series:
Each country has a cricket board. This board appoints selectors, who travel across various venues during that country's domestic season and watch a lot of players. Before any series, all the selectors sit along with the national captain and decide the merit of each top performer and select the team based on skill, consistency, requirement, team balance among other factors. Most of the top countries provide the captain (Who is again decided by the selectors) voting rights but it is not followed everywhere.
Selecting team for a match:
With the team that has been selected for the series, the captain can select any 11 players for each match of the series. The coach provides suggestions and helps the captain in making decisions, but ultimately the final decision lies with the captain.
I assume you are talking about international cricket.
The short answer is, the national board appoints a selection committee, and that committee selects the touring squad and the playing XI. The selection committee may or may not include the coach or the captain.
The actual details vary in each country. The selectors, if they are not coach or captain, are usually former players or cricket administrators. Sometimes, being a selector is a part-time position besides the person's normal non-cricket job, but sometimes it's a full-time position, in which case the actual job of a selector between selection meetings is more like being a scout or being involved in player development somehow. The chairmen of selectors is then something like a general manager or sporting director. In some cases, when the team is on tour, not the whole selection committee travels with them, but there is a selector on tour who makes certain decisions, again sometimes together with coach and/or captain. But of course nowadays they can have selection meetings by conference call in any case.
Personal note: I think it would help cricket a bit, if they made the details of this more public. The public generally knows who the captain or coach is, but the details of how players are selected and by whom exactly are often murky and only come out when there are issues.