[W]hat is the quickest way for the Republican leadership in the Senate to dismiss impeachment proceedings, if it gets that far?
The timing of the start of the trial is fixed in Senate rules.
RULES OF PROCEDURE AND PRACTICE IN THE SENATE WHEN SITTING ON IMPEACHMENT TRIALS
I. Whensoever the Senate shall receive notice from the House of Representatives that managers are appointed on their part to conduct an impeachment against any person and are directed to carry articles of impeachment to the Senate, the Secretary of the Senate shall immediately inform the House of Representatives that the Senate is ready to receive the managers for the purpose of exhibiting such articles of impeachment, agreeably to such notice.
II. When the managers of an impeachment shall be introduced at the bar of the Senate and shall signify that they are ready to exhibit articles of impeachment against any person, the Presiding Officer of the Senate shall direct the Sergeant at Arms to make proclamation, who shall, after making proclamation, repeat the following words, viz: ‘‘All persons are commanded to keep silence, on pain of imprisonment, while the House of Representatives is exhibiting to the Senate of the United States articles of impeachment against ——— ———’’; after which the articles shall be exhibited, and then the Presiding Officer of the Senate shall inform the managers that the Senate will take proper order on the subject of the impeachment, of which due notice shall be given to the House of Representatives.
III. Upon such articles being presented to the Senate, the Senate shall, at 1 o’clock afternoon of the day (Sunday excepted) following such presentation, or sooner if ordered by the Senate, proceed to the consideration of such articles and shall continue in session from day to day (Sundays excepted) after the trial shall commence (unless otherwise ordered by the Senate) until final judgment shall be rendered, and so much longer as may, in its judgment, be needful. ...
Under rule III, the trial begins at 1 o'clock on the day following the delivery of the articles of impeachment to the Senate.
After the Chief Justice is seated, a Senator could call for a vote on the articles under rule VII. The CJ rules, then some Member of the Senate shall ask that a formal vote be taken thereon, in which case it shall be submitted to the Senate for decision without debate. A majority1 voting to proceed to voting on the articles of impeachment avoids all the presentation of evidence and the questioning of witnesses.
VII. The Presiding Officer of the Senate shall direct all necessary preparations in the Senate Chamber, and the Presiding Officer on the trial shall direct all the forms of proceedings while the Senate is sitting for the purpose of trying an impeachment, and all forms during the trial not otherwise specially provided for. And the Presiding Officer on the trial may rule on all questions of evidence including, but not limited to, questions of relevancy, materiality, and redundancy of evidence and incidental questions, which ruling shall stand as the judgment of the Senate, unless some Member of the Senate shall ask that a formal vote be taken thereon, in which case it shall be submitted to the Senate for decision without debate; or he may at his option, in the first instance, submit any such question to a vote of the Members of the Senate. Upon all such questions the vote shall be taken in accordance with the Standing Rules of the Senate.
Each of the articles of impeachment are presented for a vote under rule XXIII.
XXIII. An article of impeachment shall not be divisible for the purpose of voting thereon at any time during the trial. Once voting has commenced on an article of impeachment, voting shall be continued until voting has been completed on all articles of impeachment unless the Senate adjourns for a period not to exceed one day or adjourns sine die. On the final question whether the impeachment is sustained, the yeas and nays shall be taken on each article of impeachment separately; and if the impeachment shall not, upon any of the articles presented, be sustained by the votes of two-thirds of the Members present, a judgment of acquittal shall be entered; ...
If at least 34 Senators vote "not guilty" on each of the articles, the trial is completed.
Is there a minimum duration and ceremonies to be respected before the whole thing can be put to a vote and rejecting it?
See above with regard to timing of the start. The total time would depend on the number of articles and the time allotted for each roll call vote.
During the impeachment trial of President Clinton, there was a motion to dismiss. While the trial began on January 7 (the articles were delivered January 6), the motion to dismiss was not considered until January 25. There was at least that much time used for other business (ceremonies, if you like,) before beginning the consideration of the articles.
1 Necessary assumption. If 60 votes are required, Republicans cannot control the proceeding.