Kaichou wa Maid-sama <---- highly recommend
A romantic comedy that centers on the student council head named Misaki Ayuzawa who despises the mostly male, slovenly population at her school, which was once an all-boys school. However, Misaki's most handsome schoolmate just discovered her secret — that she works afterschool at a maid café.
http://myanimelist.net/anime/7054/Kaichou_wa_Maid-sama!
Special A
Hikari Hanazono has always been second to Kei Takishima. When they were six years old, their pro-wrestling loving fathers introduced them to each other. Assuming that she was the best in wrestling, young Hikari challenged Kei to a wrestling match only to be thoroughly defeated by him. Ever since that fateful incident, Hikari swore to beat Kei in school grades, sporting events - anything. To do this, she has enrolled in the same school as Kei since elementary. Now she attends Hakusenkan, an ultra elite school, that costs her carpenter father a lot of money. Hikari and Kei are the top two students in the school, with Kei holding firmly to that number one position. While Hikari considers Kei to be a rival and important friend, she is completely unaware that Kei loves her. The story primarily focuses on Hikari and her constant attempts to defeat her one and only rival, Kei, and how she finds love in their rivalry.
http://myanimelist.net/anime/3470/Special_A
Itazura na Kiss
Ever since she entered high school, Kotoko Aihara wanted to be in the same class as Naoki Irie. The only problem, Irie is the smartest student in school while Kotoko is one of the dumbest. Now in 3rd year high school, she still isn't there. One day, her home gets destroyed and the only place else to go was to Irie's home. Now that she lives close to him, will their relationship be the same, or will it become greater than it is.
http://myanimelist.net/anime/3731/Itazura_na_Kiss
Skip Beat!
The story revolves around a young girl named Kyouko who went with her childhood friend, Shou, to Tokyo to pursue his dream of becoming an idol. Despite of supporting him, she overhears him dismissing her as boring wallflower. Furious, Kyouko vows to get her revenge to defeat him by entering the entertainment world.
http://myanimelist.net/anime/4722/Skip_Beat!
Hanasakeru Seishounen
A very powerful industrialist directs his daughter to pick a husband from three candidates he has chosen for her. They are to come into her life, and their uniqueness would cause her to recognize them immediately. All three of the candidates are outstanding. Well, it’s actually four... The story evolves along the lines of a power political mystery involving a small middle eastern country.
http://myanimelist.net/anime/5835/Hanasakeru_Seishounen
Lovely Complex
Risa and Otani are always being laughed at as the comedy duo. Risa, a girl, is taller than the average girl, and Otani, a boy, is shorter than the average boy. The two are always bickering and even their teacher sees them as a comedy act. But as their friendship develops, so do Risa's feelings toward Otani.
http://myanimelist.net/anime/2034/Lovely_Complex
Aishiteruze Baby
Katakura Kippei is in every way a high school playboy. Spending his days flirting with any female he can see, responsibility is the last thing on his mind. Life takes an unexpected turn for him as one day he returns home to find himself with the fulltime task of caring for his 5 year old cousin. Kippei's aunt Miyako had disappeared, appearing to have abandoned his cousin, Yuzuyu. With Kippei's lack of responsibility and knowledge of childcare and Yuzuyu's injured heart with the disappearance of her mother, their time together is in for a bumpy ride.
http://myanimelist.net/anime/102/Aishiteruze_Baby
Saiunkoku Monogatari
Saiunkoku is a world of eight provinces or houses, each named after a different colour. The new Emperor, Shi Ryuuki, has gained for a reputation for being uninterested in courtly matters and for flaunting his love for men. Shuurei, although born of the important Kou family, has difficulty making ends meet. She easily accepts an invitation to be the Emperor's concubine in order to turn him into a good ruler. The mysterious Seiran, a young man who was adopted by her father, goes with her as Ryuuki's bodyguard. Entering the imperial palace revives Shuurei's dream of being a court official, and, together with the many companions she meets along the way, continues moving bravely forward while trying to fend off the Emperor's advances.
http://myanimelist.net/anime/957/Saiunkoku_Monogatari
Nodame Cantabile (not sure if art will appeal to you but it's really funny)
Kimi ni Todoke (good story but really slow-paced)
Fushigi Yuugi (may be too much fantasy)
Hana Yori Dango (old art but really good romantic comedy)
Shugo Chara (not much romance but really cute)
Full Moon wo Sagashite (has fantasy element and repetitive at times, but later episodes were great)
Clannad and its sequel Clannad After Story are really excellent non-shoujo anime if you're willing to try new things. it will make you laugh and cry. one of my favorite anime.
i love shoujo anime so let me know if you have any further questions.
*edit: thumbs down? *sigh* my answer is both complete and helpful, focusing on her four criteria.