Recently I have been replacing my 2 prong outlets with 3 prong. I found out it is dangerous to have an open ground 3 prong. To update this to code I am wondering if it is ok to put a gfci in the most upstream receptacle of the circuit, so the ungrounded 3 prongs will be up to code and safer, I am also wondering if the ungrounded 3 prongs that are on the gfci circuit need to be tamper resistant? My county uses the 2014 NEC code. Any help would be greatly appreciated.
As of 2014 the NEC requires tamper resistant outlets. You are correct about how to install a GFCI at the head of a circuit and replace the old receptacles with new three pronged receptacles, But the NEC requires that the receptacles be labeled as “No Equipment Ground” . When you purchase the GFCI's those labels should be in the box with the GFCI's.
GFCIs come in several packages: combo w/receptacle, standalone, or combo w/breaker, or even breaker+GFCI+AFCI, which adds a new layer of protection against wiring faults causing fires. All of them are able to confer GFCI protection to downline parts of the circuit.
However this is not necessarily simple, and you can run into complications. Either relating to faulty wiring, or to good wiring being more complex than you are prepared to understand. This is most likely when the GFCI+receptacle device is involved.
As such, I often refer to the warning tape on your GFCIs LOAD terminals as saying "Do Not Use. For Wizards Only." That's over-intimidating, the wizard skills are perfectly reachable, but you do actually, um, have to do the part where you reach them.
We get many, many problems here where the owner never intended to use the downline protection feature, but just had a couple of spare wires he needed to do something with and randomly stuck em on LOAD. Your case differs, since you specifically want to use the downline protection, but those tangles are there just the same.
Making it easier
To start with, the dog simplest way of protecting a whole circuit is a GFCI+breaker. The breaker needs hot and neutral (it gets the latter via a pigtail), then the breaker supplies two LOAD terminals that you simply connect the whole circuit to. And you're done. It's very hard to mess this up. Success assumes there isn't some sort of crossed-circuit wiring defect in the house. If there is, then you have a bug hunt.
So I would buy one GFCI breaker, move it around, and see how many circuits it will successfully work on. Seriously consider going GFCI+AFCI combination, since that will provide anti-arc protection against your old wiring. AFCI is a silver bullet solution to a wide variety of wiring problems from old wires to aluminum wires to backstabs.
You can also get the "simpler version" by using a GFCI-only standalone. It looks like a GFCI receptacle without any holes, so it's called a deadfront. You'd need to add a junction box right near your panel to mount the device, and an extra length of cable or short conduit run to get the extra length you'd need. The deadfront has 2 line wires (those go to the panel supply obviously) and two LOAD wires (to the entire rest of the circuit). Easy peasy. Since you're adding a new location for this, you know you'll have 2 line in and 2 load out.
Once you've masterered the deadfront, it's really no difference installing a livefront (or plain "GFCI" the way most people talk). What gets people in trouble with livefronts is they usually try to install them where receptacles already are... And the wiring around those can be complex.