I will be posting the rolls for each generation here as they are revealed. I'm also including personal goals, which are not part of the rolls but just things I want to accomplish with that generation. I may not have a personal goal for every generation. But I usually do, I just have never actually posted them as goals.
NEW: Sometimes, usually by request, I post my legacy Sims for Download. When I do this, the downloads will be available on this page. Just click the Sim's name under their generation entry. Uploaded Sims will have hair and clothes from the base game or expansions, and will be stripped of any tattoos or other CC they have. The outfits they are wearing will likely be atrocious, but I expect you'll dress them to your liking in your own game. Note that I use custom defaults, so the Sims will appear in your game with whatever skin and eye defaults you use, EA or custom.

Generation Two:

Heir: Kai Brannon
LTW: Master Painting and Writing skills
Traits: Loner, Artistic, Computer Whiz, Genius, Neurotic, Handy (Nerd bonus trait), Brooding (Degree Bonus Trait)

Help: Bahir Nejem (freed genie)
Traits: Loner, Artistic, Photographer's Eye, Lucky, Diva

Children: 2

The Roll:
Family Structure: Single with Help
Number of children: 2
Primary Career: Video Game Designer (artist branch)
Secondary Career: No Income
Goal: Opportunist
Misc. Fun: Opposites Attract/Perfect Match.

Notes: As a single parent heir, Kai's Misc. Fun requirement will be filled by the co-parent of the children he will have to produce for the roll. Kai's partner in this is Alejandro Torres, who shares a matching trait (Loner) with Kai since birth. By the time both boys grew into YAs, they also ended up with a set of opposing traits, Genius/Absent-Minded.

Though it was not required that Kai's spare sibling, Dylan, also fulfill the Misc. Fun, she did also end up with a partner who shared a trait with her (Loves the Outdoors) and had an opposing trait, Athletic/Couch Potato. 

Generation One:

Founder: Jillyan Brannon
LTW: Deep Sea Diver
Traits: Brave, Loves to Swim, Light Sleeper, Athletic, Great Kisser, Lucky (Jock social trait)
Spouse: Julian (Landgraab) Brannon
LTW: The Tinkerer
Traits: Hopeless Romantic, Computer Whiz, Charismatic, Handy, Perfectionist, Genius (Extra trait from Nerd affiliation), Gatherer (Trait gained from honorary degree)
Children: 2

Kai Brannon (m). Traits: Computer Whiz, Loner, Artistic, Genius, Neurotic
Dylan Brannon (f) Traits: Loves the Outdoors, Night Owl, Dog Lover, Athletic, Brave

The Roll:
Family Structure: Couple
# of Children: 2
Primary Career: Scuba
Secondary Career: Freelance Scientist
Goal: Fulfilled
Misc. Fun: My Precious
For 'My Precious' Jillyan will collect one of each type of seashell available, and one message in a bottle. She will also make a weekly purchase of some kind of sea related decor item
Julian will be collecting space rocks.

Personal Goals:
Jilly: Max Athletic, Martial Arts, Scuba skills. Unlock as many hidden islands on IP as possible (not including the ones that require owning a 5 star resort, or the Lifeguard career). Max Jock social status. Finish the Scuba Skill challenges Pearl Diver (Collect 50 shells) and Underwater Spelunker (Explore 15 caves)

Julian: Max Logic, Handiness, Science skills. Max Nerd social status. Finish Science Skill Challenges: Free Range Scientist (Analyze 100 things) and Experienced Experimentalist (100 experiments). Also the collector challenges Amateur Rock finder (Find 1./2 of the space rocks) and Awesomest Rock Collector in the universe (Find all the space rocks)

Notes: Jillyan Brannon was actually the Gen 4 heir of my discontinued Brannon RLC. For a bunch of reasons I won't get into here, I decided I needed to make a fresh start with on a completely new blog. She and Julian, her fiance, are clones of their original selves with no skills and none of the vast wealth they had from their previous incarnation.

I did just go ahead and cheat by picking a new career for Julian. His original career was the ITF Astronomy career. I decided I didn't want to have ITF careers after all, and rather than reroll a career for him, I went with one that fit his established character. Also, I have not rolled the Freelance Science career since additions have been made to it and I just really wanted to play it. I could try to make a weak justification that the Freelance Scientist career is kind of 'new in an EP' in the sense that UL vastly changed it, but, eh, I broke the rules. Because I now have Nraas' Hacker career as separate rolled career, I will not be using hacking in the Freelance Science career. Julian will be selling chemistry potions, scientific samples and other items cloned from the science station, and occasionally found space rocks and insects for his income. Also, Correlating Scientific Data at the Science rabbithole, and maybe Solving the Unsolvable on the computer.

Progress: Jill and Julian have both completed their LTWs. Jill has also maxed her Scuba and Martial Arts. She has completed the Underwater Spelunker and Pearl Diver skill challenges, and Maxed her Jock social status (She gained the Trait Lucky from this). Jilly has completed her personal goals.

Julian has maxed his Nerd status and acquired the Genius trait, and he's maxed the Science skill as well. He's completed the Free Range Scientist and  Experienced Experimentalist skill challenges. He has completed Amateur Rock Finder.

For My Precious, Jill has been buying a sea related decor item every week. She also has an unofficial collection of one of each kind of shell that can be found (including her prize shark tooth), and an aquarium for scuba caught fishes. Julian has been keeping all his found space rocks, selling only the duplicates.