Someone from your department usually meets you, but it can vary from dept to dept. RT is not a big camp, hopefully they know the basic layout but if not its easy to find your way around. The Commissary is open 24 hours, but right now they're going through a contract change and there have been... supply issues. Hopefully that gets resolved with LuLus takes over.
Maps will be available in your home on arrival. If you have a driver who does not know where your address is located, stop and ask at the security gate as you enter. There is usually a map in their office.
LuLu will start operating in UDH on October 8th. Next will be ABQ, then Dhahran or RT (not sure which is after ABQ, but the guys in UDH are going to ABQ next to help close their store). I am not sure what dates they have set though. Even if LuLu hasn't started operating there yet, you should be able to find most basic items, such as fresh dairy products, meat (although the selection is much more limited than before), and produce (which again is more limited, but enough that you can cook!). Unlike UDH, you should be able to shop outside the compound easily, but even UDH started having extra shopping buses going to the supermarkets in Hofuf during this transition.
I don't know as I don't live in RT, but I can tell you that you should be able to find all the basic spices for Indian cooking in all grocery stores here. You may need to go to Khobar to a larger grocery store to find any specialty spices or spice blends. Don't worry...there are lots of Indians in Saudi, so you can find all the spices you will need.
Couple of points of input from a new arrival in RT...
LuLus is currently scheduled to start November 10 in RT. Which can't come soon enough as the Commissary is barren.
As for internet, Aramco DSL is available once you get properly set up at work and can request ASDL service. Your milage may vary (do non-US people say "your kilometee"?) on how fast or slow you get proper SAP access.
If you are based in RT getting internet access early on is VASTLY different than those commuting to Dhahran. You might score during new hire orientation in Dhahran and get to the STC store for a WiFi router, but service is pretty bad in house, better outdoors (not much though). Without your Iqama the in-camp Axiom shop will not sell SIM cards or any other service. Maybe a neighbor will offer up their wireless password or such, but you might plan on 2+ weeks of no internet to start.
LuLus opened November 10 in RT. Amazing what a proper commissary can be in comparison to last month. Prices seems fair to what you see at Panda. Meats and Produce also of good quality. More investigation needed, but LuLu has started off on the right foot.
As a side note, you can buy prepaid SIM card recharges at the register, so once you get going with a local phone you can recharge minutes without leaving camp or needing a Saudi credit card.