How do I choose a property type based on budget, yield, and liquidity?

You can simplify the decision in three steps: set your total buying limit, decide whether the priority is recurring income, growth, or personal use, and then define how quickly you may want to exit in the future.
The more you need liquidity and flexibility, the more apartments make sense.
The more space and family lifestyle matter, the more townhouses and villas become logical.
Do not buy what the market is talking about; buy what fits your budget, use case, and future exit plan.