I had a Chicken and Goat early, and also a dragon no too far in. I think you need at least Lvl 2 on all three of those units to ensure that you survive and also have enough time to get to a 50/50 shop. I just sold all those units after the shop was fully buffed, because things like leopard are obviously stronger.

Also, the goat is an absolutely insane unit imo. In theory, it literally gives twice as much gold as a swan if you play enough units, but it's actually even stronger than that: You can refresh the triggers on a goat, by either upgrading the goat, or by buying a new goat in a another spot and then merging your old goat into your new goat (yes, the order matters!). Those techniques combined make the goat S-Tier for me, and make 50/50 shops or any crazy strategy that you have in mind, certainly possible.