It's really hard to say what is definitely best, but I will add my meagre advice and hopefully something with resonate with you. It's really hard to say because it depends entirely on what your goals / values are and what your risk tolerance is. What my be the best decision for you may not be for someone else.
First of all, I don't think there's necessarily anything stupid about liquidating investments to purchase your dream home, especially if it is undervalued like you think it is. You need a place to live, and if your current home is going to to become a rental then you are essentially just trading types of investment, from stocks / bonds to real estate. Traditional investing advice applies here too, if you can "buy low" on your new house then you should. If you can potentially turn around and sell if for 2x what you paid for it then you almost definitely should, although if this really is your dream home and you plan on living there indefinitely then the potential sales price is less relevant.
As for which account to take the money out of, or whether to take out a HELOC, the mathematical answer is that you should take the money out of whichever source has the lowest interest rates. If you expect the stock market to return 7% per year, and the HELOC would be 4.25%, then it's mathematically cheaper to take a HELOC than to withdraw from your investments. However, mathematics are not the end of the story because there are varying levels of risk involved. The stock market is fairly volatile. By withdrawing your invested money you may be avoiding a huge drop in value, or you may be missing out on a huge increase in value. There's no way to know. The HELOC should be very stable by comparison.
If it was me I would use all of the $30k that you have in savings (unless you are saving for something in particular that is coming up soon), take out the HELOC for the other $30k, and leave as much in the investment account as I could. But if you were more risk-adverse then withdrawing from investments before taking out a HELOC is equally valid. It's true that rental income would allow you to build up investments / pay off debts faster, but that is true regardless of how you fund the initial purchase.
Anyway, I hope you find some of that rambling useful.