How should one saves up for a house? should one be saving up for the initial downpayment? or also the subsequent loan payment as well?

We only saved the downpayment for our properties. The loan repayment paid from our salary. We make sure the loan repayment only take up less than 20% of our salaries.

Rule of thumb for house affordability is 5 - 7 times combined annual income of you and your spouse, so from there, work out your current max amount that you can afford and use that amount as an arbitrary number. For example say the max amount is 800k. Then you have to work out if you want HDB loan or bank loan.

HDB loan you can borrow up to 90% of the purchase price, the remaining 10% can be paid using cash or cpf.

Bank loan you can borrow up to 75% of the purchase price, and at least 5% of the remaining 25% must be paid only in cash, the rest in cash/cpf.

Estimate roughly how many years you expect to get your house, then work towards saving/investing the downpayment amount.

For the subsequent loan repayment, you can pay part of it using CPF part in cash. For this I recommend to increase your work income through personal development and upskilling so that you can increase your cpf amount and be able to afford your monthly repayment.