Well the story needs some work. As you said you borrowed ideas from other stories but they are presented in a crude manner. First of all you have to establish a few things before beginning writing. What is the purpose of the show? Who is the audience? What do you want the audience to take from the show? (This is a subset of the purpose of the show).

You also want to have an outline, which it seems you do even if it isn't written, this should include the four basic parts of the plot; Intro, conflict, climax, and resolution. Also on a micro scale each episode should have include the parts as well where applicable. The conflict is probably going to be the substance of the story; you'll want to have multiple types of conflict, man v. man, man v. nature, man v. self etc. There should be sub conflict as well as sub climaxes and sub resolutions. You should also have a point of view, objective, first, third, omniscient. Again you will want to have variety, you will probably be spending the most part in an objective point of view with brief moments of first and narrative. From the little part of the story you have made available you have some of these elements but the depth doesn't seem to be there.

The characters are an important part of the plot; you want to create a connection with the audience. Your main character achieves this by being "average" and one day find special powers, which isn't a bad thing, but it is used a lot. You also don't want to pigeon hole your characters into stereotypes, a character should exhibit stereotypes but he shouldn't be a stereotype. You will want to play with the audience through the characters, make them hate/love the character either by what they do or how they are. I don't mean make the character obnoxious like Relena in Gundam Wing, and only repeating the same thing 50 times an episode. A good example would be Ed from Full Metal Alchemist, you have times when he does thing the audience hates and makes the audience yearn for the conflict to end in the perfect fairy tale way. The characters should have a goal and personality to create the connection.

You are probably still wondering what specifically I didn't like about the story. First of all, the characters, the names are in my opinion too bland, the matching names aren’t a good trait. Also the characters seem to be one dimensional, this may change as you only told the basics of the plot but that is my impression. You could consider removing Lee and combining Luna and Lee, obviously this would screw up a lot of what you have written but I'm just throwing out ideas. If for instance you have Luna being the intended pilot of the Alpha mech with Sol taking her spot you will create two conflicts, man v. man (Sol v. Luna) and man v. self (Sol v. self). I suggest this as the coordinators seems more as an informative sub character and from just what you wrote Lee disappeared. Next, you could also change the whole Sol magically pilots it perfectly; this is an area that is over used in my opinion. I don't have a suggestion on how to change this right now as you want the fantasy part of it where the audience can have the 'winning the lottery dream', and having the character struggle right off the start would eliminate that.

Writing a good story isn't all that easy, there are lots of thing I have probably forgotten or just don't know. However, if you want to create a good story you will have to put some time into it, and change it a lot. Have a friend or family member read over it and give you feedback and continue from there. You made a good start, but revision is always a good thing.