Do not use MTA race, race is very old, before MTA SA (which is deathmatch, race, everything else) was done. Just host an MTA SA 1.0.5 server and "start race" command.
Modem should work and you won't have to even port forward so just get your IP address from http://whatismyipaddress.com/ and as long as the server is running and there is a firewall exception in place it should work.
"Take it from there?" Well its written in C++ and as JR10 said, its hard coded which means it will always be available for use in MTA as long as it is not disabled in the ACL.
Just start admin resource so you can use /register
Then login to the account and assuming you correctly added the account to Admin in your ACL you will have access to do things.
Remove editor_dump and editor_test from the server/mods/deathmatch/resources folder and try again.
If that fails then your map file might be corrupt, but its most certainly the above issue.
I made CIT mainly on my own. What you really need is:
1) A vision
2) Motivation
3) Determination
4) A bit of money
5) Security paranoia
6) Experience scripting
7) Leadership
How many players do you plan on having? I'm not sure on bandwidth usage of smallish servers but CIT which peaks 230 players in the day and probably doesn't go much below 80 at night will have used that 250gb in 1 day as it has done today.
I don't think the average server will use 250gb in the whole month though.
There was once or twice a report of serverffs being very improfessional, the owner of the company being involved in those reports so I wouldn't recommend them for anything more than hosting a small server (if your server was popular he might just feel like having it)
Don't take my word, or anyone elses word for it though. Read reviews and search the Internet for any reports against them like the ones I mentioned.