If you are on a tight budget, buy a second hand machine that is built to last like a Gaggia classic or a Rancilio Silvia. And put in a PID. You might even have enough change to get a big ugly but very effective ex-commercial grinder like a Gino Rossi.
But Im just recommending exactly what I bought faced with a tight budget.
If you do want to buy new, Cosmorex has the classic but if you buy it new you wont have money left for a grinder.
I dont know anything about the gaggia baby, someone else will chime in on that.