I have a default field in the project.task.type model to define that the stage is on a new project and normally another many2one field to define the stage usage. 

default_stage = fields.Boolean(string='Stage on new project', default=False)

Then I just extended the project create method to add the default stages to new projects.

@api.model
def create(self, vals):
    ir_values = self.env['ir.values'].get_default('project.config.settings', 'generate_project_alias')
    if ir_values:
         vals['alias_name'] = vals.get('alias_name') or vals.get('name')
         # Prevent double project creation when 'use_tasks' is checked
         self = self.with_context(project_creation_in_progress=True, mail_create_nosubscribe=True)

         default_stages = self.env['project.task.type'].sudo().search([('default_stage', '=', True)])
         stages_list = list()
         for stage in default_stages:
            stages_list.append((4, stage.id))

         if len(stages_list) > 0:
            vals['stage_ids'] = stages_list

         new_project = super(TablaProjectProjectExtension, self).create(vals)
         return new_project 

Try this code please :)

from odoo import models, api, fields, SUPERUSER_ID, _

class ProjectTaskType(models.Model):
	_inherit = 'project.task.type'

	# Step specific code to identify it
	code = fields.Char('Code')

	_sql_constraints = [
		('code_uniq', 'unique (code)', "Stage code already exists!"),
	]

class Project(models.Model):
	_inherit = 'project.project'

	@api.model
	def _read_group_stage_ids(self, stages, domain, order):
		# Call Super Function
		response = super(Task, self)._read_group_stage_ids(stages, domain, order)
		search_domain = [('id', 'in', response.ids)]
		# Append my specifik stages [Stages whose code is equal to todo or inprogress or done or canceled]
		search_domain = ['|', ('code', 'in', ['todo', 'inprogress', 'done', 'canceled'])] + search_domain
		stage_ids = stages._search(search_domain, order=order, access_rights_uid=SUPERUSER_ID)
		return stages.browse(stage_ids)