I don't want to cut myself short on the investing side of things
Then break out the calculator (and someone please correct me if I'm wrong):
Let's assume you end up with $200k that you can't decide whether to invest it or pay the house off.
Assuming you invest it and finance $200k for a house at 5% for 15 years, your payments will be around $1600, which results in about $285k in payments. Meanwhile, your $200k investment with no additions will have grown to about $490k after 15 years (assuming a modest 6%).
Now let's assume you use that $200k to buy the house, and invest that extra $1600 per month you will have instead. After 15 years, you will end up putting that same $285k aside, but it will have only grown to about $465k.
So, 15 years on, you will have a paid-for house either way, but by investing you will have an extra $25k. And that's with the very tight percentage spread I used. You can probably get lower than 5% on a mortgage, and you will probably average better than 6% by investing wisely
. Whether that's worth the trade-off for peace of mind by not having a mortgage is up to you.