As far as judging philosophy goes, I do not have particular preferences. I believe that debate is a place for discussion and discovery. Respect and politeness is a very important part of a good debate. Below is a briefing of how I look at each speech/area of the game, for both Public Forum and Policy (shorter for Policy as I assume you are pretty experienced if you are debating Policy).
Cross-fire – Be polite, be persuasive, and don't beat around the bush. This is not the time for quarrel or to read off new arguments, but it's for answering your opponents' answer directly. I will not flow cross-fire, so if your opponents conceded to an argument or you think you made a great analytic, you need to mention it specifically in your speech so that I can take note of it. Ask good questions! Closed ended ones are always better than open-ended or clarification questions.
First speeches – There is no need to have a Framework, but it will definitely work for you if you utilize it throughout the debate. Often, people read framework just for the sake of reading it, and fail to develop it beyond their first speech. In short, it is a very powerful tool that debaters should definitely consider using and if you're not using it, don't bother reading it in the first place. As far as case goes, any type of arguments work for me – unless it's illogical or very offensive. But I expect that close to half of the arguments you read in the first speech would be extended into the debate, or else reading that one card is just a waste of time if you don't take advantage of it later in the debate.
Second speeches – The most important roles of the second speaker is to attack the opponents' case, defend their own side, and potentially build upon their case by reading add-ons or additional arguments. The order you put these burdens in really depends on how you are taught, but generally it is most effective to put your rebuttals first and case last, with more time spent on your case. Anyhow, I'm not picky about the order, it just have to be strategic in the debate. And again, if you have a framework you should definitely extend it right in the beginning of your speech.
Summary speeches – This is the time when debaters must funnel down the arguments of the debate for the judge. If you do not list out the most important arguments, it becomes time consuming for me to look through the notes and I might miss an argument that you believe you have won on. Don't feel obligated to extend every answer or argument, just explain to me which are the most important arguments and/or clash in the debate. What's even more strategic and effective is to start your impact calculus here, so that there's less work for the Final Focus. A final note is that I shouldn't see any new arguments in terms of contentions (new answers to the opponents are okay). Also, if you shadow extend any cards (meaning you only read it in the first speech not the second speech), I may or may not vote on that card. But if the opponents never addressed that inconsistency, then I will just let it through.
Final Focus – Here is where you want to limit down the debate to that one or two arguments you think you have won on. There are many ways to do this, but no matter what, it should be clear, concise, straightforward, and easy for me to follow. In the end, the more work you do for the judge means the more likely the judge will vote for you. Impact calculus is also very effective here. In short, no new evidence, elaborate your arguments (including your framework if you extended it throughout the debate), persuasion, and a story to sum things up if possible.
Framework – like Public Forum, framework should be included in your speech unless you have a good reason not to do so. Develop it, use it to your advantage, and extend it across your speeches so that I will take this into consideration when deciding the ballot.
Topicality – if you do not extend it across the your speeches, I will disregard it as an argument, and be sure to include all of the necessary components. Again, this is a tool that can win you a debate.
Theory – must be explained clearly, efficiently, and logically if you're going to mention it.
Kritiks – only run them if you know how to explain them from the inside out. Have a strong link and don't rely on prewritten blocks. You can always tell when a debater doesn't understand a kritik they're running.
DAs – be strategic when running them, especially when paired with a CP
CPs – always have a net benefit to the CP, answer each permutations separately, and be strategic.
Prep – email/flashing is not considered prep, but if it takes an unreasonable amount of time, then down goes your speaker point.
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(work in progress)
Above are more like the logistics of the debate. As far as skill, persuasion, and speaker points go, just do your best and learn from your mistakes because it's not something that can improve in a day, but as you have more and more experience.
Good luck and have fun!