If you're not going to be streaming or uploading YouTube videos, then the first plan will be the best in terms of overall budget and performance. If you are uploading or even want faster speeds, 1GB is going to be the best for gaming. HOWEVER, when calling, ask if it's Gigabit or Gigabyte, because it does matter. 1 Gigabit is only 125 MB, which would better fair you for the first one that is $70 a month.
Going back to since you're on console, if the second option is 1 Gigabyte, I don't think you would be able to utilise the full Gigabyte internet all the time. Consumer Ethernet ports come in 10/100/1000. Anything going over 100Mbps at times can be a luck of the draw because the server closest to you may not support that high of bandwidth. In reality, you could get either internet package and be downloading 100 Mbps for games and updates. Sure, a test of your speeds can show you are getting the speeds advertised to you, but doesn't mean you'll download at that rate. We'll hop over to Origin for example. I get 350/350 internet right now (was 500/500 but Cox messed something up.) Steam lets me download at full speed, however Origin caps me out to about 100 download speed, even after messing with the settings. Their servers are throttling it either because they don't support that bandwidth or there is too many people on one server that I'm connected on, using it up.
If you were gaming on PC, I would tell you to get the 1gb (after confirming if it is 1 Gigabyte or 1 Gigabit.) PC gets updates for games a lot more than consoles do, where having that extra speed would be better for you. It would allow you to download/torrent at faster speeds, while still having room to spare for browsing the internet or updating/downloading a game without tanking your speeds. Console however, doesn't get updates as often and like I said before, getting to use the full speeds is a luck of the draw if it will allow you to download/update at those speeds. The first option for $70 is going to be right in your zone. You mention you're on a budget, so that saved $30 a month adds up to $360 saved a year, which you can use for numerous things.