Most instances would federate with you immediately since they're on a blacklist model, but some instances (such as awoo.space) operate on a whitelist, meaning they'd have to vet you first.
That still leaves postgres, redis, your web server and all other system processes. Fitting those on the same server with a total of 1 GB of RAM available is a very, very tight fit. You will probably get OOMs regularly, and upgrading Mastodon, doing backups and things like that will be painful (building assets, for example, tends to eat a lot of memory).
hugogameiro, from what I understand, runs a lot of mastodon instances on shared infrastructure. That eliminates a lot of that overhead and if you look at just the instance-specific processes, 1 GB seems realistic. If you have existing infrastructure (i.e. something like postgres, redis, nginx) and can allocate about 1 GB of RAM to Mastodon, or use something like a Heroku 2x dyno, where these components are separated as well, that might work. Otherwise, I'd opt for 2 GB of RAM.
I did indeed hit OOM during the setup (`bundle install` and `yarn` steps). After the first one I added a 1G swap and made it all the way through the 1.6.1 install (although the webpack precompile step damn near used up the whole swap!). Anyway 1.6.1 idles around 600M without any attempt to optimize.
I next tested an upgrade from 1.6.1 to 2.0.0 and was able to get it done (with the precompile again cutting it close - it hit 1015M of the swap, hah!). No change in memory usage, perhaps a bit more even.
Off topic - the install process was easy enough but seems like it could really do well to be (much) more automated. Do you know if anyone is working towards this? I suppose that is what Docker is for...