How to contain once you have map control?

I played SC1 recreationally, but I am a pretty heavy gamer. I decided to pick up SC2 and play it hardcore, so here I am. I've only played some 20 ranked games, but I've done loads of research and watched a lot of commentaries. I am only in gold currently, but have won 70% of my games. Nothing too great yet, but I'm learning quickly.

I play as a terran, and I have been working to perfect my 1/1/1 opening. Many times I have been able to gain some pretty early map control and set up outside the enemies base with a force of a few tanks, 10+ marines, a couple vikings and maybe a medvac. I scan/scout to see that they have a similar sized force, and being that my micro with tanks needs to be improved, I don't feel that I will win the battle if I try to push up the ramp. Therefore, I would like to do what I have heard/seen from many people which is simply contain them and then outmacro (or run them out of minerals).

So, my question is, "how can I , as a Terran, most effectively contain a turtling enemy sitting on 1 base." What can I do to ensure that I get a victory here. I know of lots of things that would be "ideal", but often times with a low apm I have to choose the most important actions and execute them.

Should I build more marines/Tanks/Vikings and just wait it out?
I need to keep them from dropping at my base/sneaking out to claim an expansion, so should I make sure I get some sentry towers up?
How about turrets instead of sentries so I can be warned of cloaked banshees trying to harass?
I've already expanded once, should I grab a third & attack knowing that I can just macro them into the ground since they only have 1 base?
Maybe I should just mass up a quick fleet of 6+ Battlecruisers and try to make a push after they are done?
I would like to harass, but I find it hard as they have usually posted cannons/turrets/crawlers because of my earlier harassing (and the fact that they have been forced to turtle).

As I said, it would be ideal if I could do all of those things at the same time, so what should I focus on. I need to have a list of some important things once I get my tanks/units posted up outside their door (and I'm comfortable their push won't kill my army at their door).

Thanks in advance!

 

I'm not so great at Terran, but as a Protoss player I can tell you some things that I find difficult to manage -

Lots of siege tanks. If you already have the player contained then set up a good amount of siege tanks (around six becomes close to "critical mass") spread out enough that they are difficult to focus down. Supplement the tanks with MMM (marine, marauder, medivac) and go for vikings if you see colossus. That combination will be very difficult to counter.

If you want to remain aggressive and end the game quickly, you should continue to push your siege tanks slowly towards their base. Eventually you will be able to attack his units/structures from a distance forcing the player to either move in or lose structures. This is a very good way to stay in control of the game.

Continue to scout around the map periodically to ensure they have not sneaked (snuck?) any expansions.

 

You can use an aggressive Sensor Tower or two in order to make sure that no drop ships are leaving (whether they are filled with units or SCVs for an expansion). If they are trying to get one out, just shoot it down with your Vikings.

 

If a player is hell bent on playing turtle I say let them and I would even let them expand as well. Let them spend the money on expanding only for you to kill it half way through it's build. If they are turtling then they aren't going to send units to protect it, especially if you have the end of their ramp zeroed in with your tanks.

More then likely they will be building an air force if they are playing turtle so build some air units and do whatever you can to make him have to spend those precious minerals.

Build a couple of battlecruisers and research the Yamato so you can hit parts of his base from a safe distance. This will draw out his air units and you can counter that as well.

As long as he is giving you the time get your nukes, that always adds fun to a game.