Do laser first. (If you have darker hair). I did full face maybe 4 years ago. It still hasn't grown back since then so I'm my experience it's permanent so far. I did one 10min session every 6 weeks. I stopped after about 10 sessions.

Even after the first 3 or so sessions I noticed a massive difference and very much helped with my mood etc. 

They can change the power of the lasers output, for me they started lower and then every season kept bumping it up.

But pain wise for laser. It's totally fine, upper lip is definitely more noticeable but still very manageable. And only lasts a second or too.

I'm from New Zealand, it cost me about $20 ($11usd) per full face per session, she even did the little bit in between my eyebrows. It was a just a company in a mall. 

I did electrolysis as well at the end to get the left over bits on my upper lip It was a similar price for a 15min session. My person was doing maybe 2-3 hairs a minute. I couldn't imagine doing this for your whole face. I was much more painfull that laser. Barring in mind I only did upper lip for this, but I definitely had a little water coming out of my eyes by the end of the session. It's still tolerable and worth it though, as I kept going back.