This is a little complicated. How each race starts is determined by the galaxyScenarioDef.galaxyScenarioDef file, you'll need to change several things:
First, you need to add your race as a playerType, scroll down to where TEC/Vasari/Advent are listed:
playerType
designName "Tech"
entityDefName "PlayerTech"
And add your own, make sure to increase the playerTypeCount since you added one. The entityDefName uses the name of your playerrace.entity file.
Next, scroll down a few lines to find:
planetItemsTemplate
templateName "Template:DefaultHomePlanetSetup"
Currently it has 3 groups, one start for each of the default races. You'll need to add a 4th group for your race, just mimic the way it's done. Also increase the groups count, of course

Now, if you created custom ships/modules for your race, it gets trickier - if you look above where the playerTypes are listed, you'll see planetItemTypes, these are how the game knows what's what. For example:
planetItemType
designName "Psi:CapitalShip:Colony"
entityDefName "CAPITALSHIP_PSICOLONY"
This means the game knows that whenever it sees an item named Psi:CapitalShip:Colony, the corresponding entity file is CAPITALSHIP_PSICOLONY, which is the file for the Progenitor Mothership. So if you were to change the PSI starting template from:
group
condition
type "PlanetOwnerIsRace"
param "Psi"
owner "PlanetOwner"
colonizeChance 1
items 3
item "Psi:Module:FrigateFactory"
item "Psi:Frigate:Constructor"
item "Psi:Frigate:Constructor"
to
group
condition
type "PlanetOwnerIsRace"
param "Psi"
owner "PlanetOwner"
colonizeChance 1
items 4
item "Psi:Module:FrigateFactory"
item "Psi:Frigate:Constructor"
item "Psi:Frigate:Constructor"
item "Psi:CapitalShip:Colony"
The game would have the Advent player start off with a Progenitor Mothership.
So if you added custom units/structures and you want to modify game start, you'll have to add those planetItemTypes and stick them in your race's DefaultHomePlanetSetup template.
Hope this helps, if you have any questions feel free to ask! Make *sure* your counts are correct, the game will crash horribly if they aren't