Of course you can walk around downtown

Arriving is the simplest thing. Buy a visa from one of the banks immediately before the immigrations desks, stick it in your passport and join the immigration line. There'll be no hassle or hustle, though once you're through the passport business someone from a limo company might ask you if you need transport.

You really don't have all that much time, and as you are nervous you might follow the advice above and stay at the airport Meridien (it's attached to T3). There's a (considerably cheaper) Novotel on the airport: this hotel will arrange a meet, greet and 5-minute transfer (no charge, but a tip will be in order).

If you want to fill your time, you could consider the Intercontinental at Citystars, just a 10 minute drive from the airport. This hotel has a superb spa/health club/gym and it's attached to a massive upmarket mall. They'll arrange a meet and greet for a substantial charge. Or you could get a car from the limo desk at the airport.