Hollow Area Tutorial, choose to watch the explanation of what has occurred
Once back in the Floor Clearing hub (Arc Sofia), go through anything they tell you too (I believe you have to go back to the Hollow Area quickly before getting free reign)
Do Floor 76 and maybe 77 (don't forget the side quest guy who gives side quests each floor until floor 97) to get your bearings. Feel free to mess about with skills, using different weapons, etc. Up to you really but it's a good way to start off slowly.
After this, feel free to head to the Hollow Area and look for big monsters to fight, ones that are 20 - 40+ your level even

.
If you reach Floor 90 before you finish the Hollow Area, beat the Hollow Area right afterwards. (or at least before you finish the game but doing it at floor 90 sounds good to me. Will also help level you up for floors 98 - 100)
If you're going for all trophies, (spoiler on a game-only character)
Grind Streas relationship rank to 5 and see her bedroom scene before floor 95.
Otherwise you're screwed til NG+ HOWEVER relationship ranks carry over to NG+ if you decide not to get all trophies on your first playthrough. Also make sure to get the Last Attack bonus if you're going for trophies. If you fail to get one, quickly exit the game at the result screen before it auto-saves. (same if anyone dies during a boss fight since there is a trophy for no deaths during boss fights as well) You should also not sell any Last Attack bonus items. I read on the PS Trophies website that you must have all of them to get the trophy but I can't confirm this myself at the moment.
Also small tip: Never underestimate the power of items, both buff ones and healing/SP related ones. The regenerative SP ones helped me a lot near the end with a few side quest level 180 enemies

.
Another small tip: SP Multiplayer Mode will help a LOT during the early parts where several characters are lower leveled like Silica, Sinon, Leafa and Liz
And another Small tip: Look around in the Skill list, there is 2 skills you can learn that will be useful, one increases your XP and one gives XP you earn to your party member which helps both grinding Kirito and Grinding whoever you're partied with. (I think it's in "Scout" in the skill learn window?)
Some might disagree with the start of things but I do think Floor 76 - 77 are good to do at the start while you're getting used to the gameplay systems before fighting some of the tougher enemies (especially level wise) that you'll see in the Hollow Area
edit:
AI tip from names2hard4you:
But maybe this will answer your question, each Heroine specializes in a different weapon and each one has their own set of skills and stats. All skills fall under 3 categories, ATK, BUFF and DEF that you can switch by talking to them on the field. By issuing commands and saying "nice!" after they perform a skill under that category, you will be telling her that she did exactly what you wanted, therefore nurturing her AI making that skill more likely to occur in a given situation or when you issue that particular command.
Related AI tip also from names2hard4you:
Focusing on one of the 3 branches and getting the little pentagon shape under her "character info" past the grey line unlocks a specific costume for her. I would say focusing on AI is good not only to have a reliable partner in battle but also to get her costumes. After you get all 3 you unlock the ultimate one automatically.