The Adventure Begins

Pidgey was hit by the move, it flew back and then attacked Eevee with tackled.

(gonna use a generator)
Reina saw a Bellsprout nearby, she sent Riolu at it. It was level 3, like Riolu.
"Quick Attack!" Riolu sped at the Bellsprout and used quick attack, while the other Pokemon attacked with Vinewhip.

Chloe gasped "Eevee dodge!" the pokemon just narrowly missed being hit with the tackle "tackle again while it's still close to the ground!"

Pidgey was tackled by Eevee and was starting to look a little more weak. It used San-attack to blind Eevee.

This time the attack hit and Eevee started to try and rub the sand out of it's eyes with her paws "awe Eevee, are you alright? Can you see?" Eevee managed to open one eye and nod "blind him back Eevee with your sand attack" hoping that this would weaken him enough to catch him.

Pidgey couldn't see due to the sand in its eyes.

Meanwhile, Riolu used another Quick attack on Bellsprout who once again attacked with vine whip.

"Eevee tackle!" she stated once more, to make sure that the pidgey was weak enough out catch, Eevee still had one eye closed but she ran directly towards the Pidgey.

If Eevee's attack managed to hit, Chloe would pull out one of her tiny pokeballs, pushing the button to make it bigger and toss the ball towards the pidgey, crossing her fingers that she managed to catch her very first pokemon.

Pidgey was hit and now much weaker, the Pokeball thrown at it managed to catch the bird.
(Pidgey was caught, a nickname and personality?)

Meanwhile, Riolu managed to beat Bellsprout, getting 3 EXP points and leveling up.

(personality - has an attitude, and will only fight in a battle if he feels like it. No nickname)

Chloe cheered, clapping "I caught it! I can't believe it" she was clapping her hands with excitement before turning her attention to Eevee's eye that still had sand in it. Helping wipe some of the sand out of her eyes until she was able to open her eye again "there.. by the time we get to Cerulean City, you'll be more than ready for that badge"

Reina smiled, "I don't mean to bother your, but isn't it better to face Brock before you face Misty?" She asked.

She paused, turning to Reina "Brock? is he.. easier?" she asked, seeming a little unsure.

"Yeah...his Pokemon have lower levels." She told Chloe. Riolu was busy walking ahead of them, pointing that they had to go through Saffron City.

"hmm.. he has rock pokemon doesn't he? water pokemon are what's best against him do you think I should try to find some water pokemon on the way?" Eevee huffed slightly from the ground as she walked beside the two "Vee.." as if to say that she could easily do it without the help of a water pokemon.

Bulbasaur smirked, she walked next to Eevee.

"Well he uses Onix and Geodude, they're both ground and rock types...so fighting, grass, water, steel, ice and ground." She concluded. Riolu, closed his eyes, using his aura abilities to find the way out of Saffron City and towards Cerulean City.

"oh.. well we should definately find some on the way then. Then we should head to um.. Pewter City right? That's where Brock is.. maybe we can find a day care on the way, I'd like to see if they'd have any unwanted pokemon.. my father told me that sometimes abandoned pokemon get put there"

"Yeah, There's also an adoption center." She told her. (in the Pokemon Market xD)
They made it out of the City and were on another route, this one leading to Cerulean City.

She follows her down the next route leading it's way to Cerulean City, this one looking much more familiar to her.. she paused, seeing the grass next to her rustling around.. "Eevee.." her pokemon paused to look as well as Chloe stepped closer to see what was making the grass move.

In the grass was a wild Caterpie level 5!

"Eevee look a caterpie! Use a tail whip" she commanded and Eevee jumped to it immidiately looking confident.

The Caterpie was distracted by the tailwhip and watched Eevee's tail move instead of attacking.

"now tackle him Eevee"

her pokemon moved quickly slamming her head into Caterpie's body with an impressive amount of strength.

The tackle was a critical hit and Caterpie lost a lot of HP it attacked back with tackle.

"alright that's enough Eevee.. pokeball go!" she tossed the ball at the Caterpie and watched as the pokemon got caught inside of it, waiting to make sure that the caught was permanent.

The ball absorbed the Caterpie, capturing it.
(Personality and Nickname? It's female too!)

Reina clapped, "Nice, don't forget to train your Pokemon too." She told her.

(No nickname. Personality: happy and carefree)

She smiled excitedly, "as soon as we get to a pokecenter and get their strength up ill take them all out.. id really like to find a water pokemon"