Offer accepted on flat, deciding on best way to finance it with savings

I’ve had an offer accepted on a flat, 135k, and I’m trying to decide how to finance it. Of course I’ll need a mortgage and I have substantial savings of around 120k (split between LISA, ISA and normal savings)

Initially I thought about dumping most of it straight into the mortgage and paying it off ASAP for the psychological benefits but that doesn’t feel as safe as it sounds.

I’m early 30s with plans to travel etc. I also only have a small pension built up. So my other thought was putting 80k into mortgage of 25 years, 15k into emergency funds and drip feeding the rest into S&P 500 (around 1-2k a month).

I will continue to earn around £2k a month and also plan to get a lodger so that’s an extra £600 a month I could invest/save. I’m not overly happy in my job so it would be good to have the funds to know I’m not stuck and also build a travel fund for a potential year out in my mid 30s.

How does this sound or am I missing anything critical?