I think that there are a few things you can focus on that will improve your chances of winning. In no particular order:
- Take cages that allow you to use imps for other purposes. These are the cages that feed/play with/clean up after your pets without needing imps. If you need to hold back imps in order to deal with your pets, you aren't using them to gain additional resources. This can also be accomplished with add-ons, but don't rely on them.
- Take additional imps when possible (but don't pay too much for them). This is especially handy in round three and four where you get a high rate of return. I wouldn't ever take this action using more imps than the number you will get back. This is especially true in later rounds
- Take pets that are omnivores. This allows you to take either meat or vegetables, making it less likely you'll be fighting over resources with other players.
- Try to get two pets in the first three rounds. This will help with both exhibitions and business.
- Decide on one of two strategies for your need cards early on. (1) Keep as many of one type of need card as possible (e.g.: hunger needs; anger needs). This is a high risk/high reward strategy, where if a customer wants a trait you have a lot of, you can get a good sale. In this case, you also need to allow for the possibility you aren't going to be selling pets to certain customers. (2) Diversify your need cards as much as possible so your pets can be acceptable to a larger number of customers. The reward here is lower, but more consistent over the course of the game.
- Ignore the hospital unless you have imps that need healing. The potions generally are not worth the imps. You could instead be setting up for the market by adding an imp to the platform, or taking artifacts that have a higher likelihood to be helpful over the course of the game.
You'll notice that the first three things have something in common: they allow you to maximize your imp usage. The more free imps you have, the more actions you can take, so the more resources and options you're going to have.
If you're noticing a player that consistently places a bunch of imps on the first burrow so they can take the first action, let them. They are taking fewer actions over the course of the game and paying a premium for those actions. You may want to overpay in rounds one or two so that you can get the cage that saves you more imps down the line, but don't do this for the whole game. If you set up well at the beginning, you shouldn't have to overpay in rounds three, four, or five.
Try not to worry about the color combinations of your pets. You're going to be drawing a need card for each of their colors anyway, and in general, this is going to be an aspect of the game that's hard to control. Focusing on other parts is probably more important.