What would be the best way to save money for a new house? CD?

TL;DR – Saving for a new House. Need to save around $30k total. Currently saving about $1,300/month. Best way to save/grow money? Savings Account: 3.057%, CD: 4.65%, Alternate Choice I haven’t looked into yet?

We currently live in a house we purchased at 2.8% and have about 20 years left on the loan. This is more of a starter home and we would like to move to a slightly bigger home in a better school district. I’d like to turn the current home into a rental and move into the new one in the next 2-3 (even 4-5 is fine) years.

The area we are looking at has new builds in the $500k range. I’ve looked at used houses around the area and they are all in the $600k – $700k range. Don’t know why it costs more to buy used than build new, but if I have the time, I don’t see why I wouldn’t just build new.

The current house needs some minor repairs and could probably be touched up with new flooring/replaced carpets for a few thousand dollars. Estimating we need to save about $30k to out down and we currently have about $4,000 in savings. I looked at our finances and I think going forward, we can save about $1,300 a month. My bank offers a 4.65% CD right now. Keeping the money in a regular savings account yields 3.057%. Should I start putting money into the CDs to save, or should I be looking into some other way to save/grow my money for a new house build.