There's nothing to prevent you from changing aircraft part way through but the change will set you back a bit as you 'convert' to the other type.
The hourly rate for the instructor may not be much less than the rate in their aircraft and with the costs on top for your own machine may work out more expensive.
If you qualify in a Eurostar you'll need some of this training anyway as you convert to your own as it will handle differently.
I don't think there's a clear answer as both ways are fine and unless you know how many hours you'll neeed for your licence and conversion then it's hard to work out the costs.