When the T-800 visits the gun shop, his "home defense" excuse is actually true from a certain perspective — he's buying the guns so he can make sure his "home" (Skynet) is safe in the future.
According to Reese, the reason why the Terminator was being systematic and going after Sarah Connors in general by following the phone book is because Skynet didn't have any information on John's mom. This makes sense when you consider that before computer systems became commonly used for data input and processing, most records were stored as hardcopies on paper. So unless those hardcopies were transcribed or scanned into a computer system, those records may have been lost due to the nuclear war breaking out and destroying them. This also explains why the Terminator used the phonebook, because it was being sent to a period of time where it could more than likely find readily available information on Sarah Connor (and anyone named as such).
It's a bit odd that In-Universe the T-800 would pick such a thick Austrian accent when he could easily try a more common American accent, isn't it? Not when you realise that most bystanders would likely think someone with so thick a foreign accent would be either a tourist or an immigrant, thus excusing some of his more glaring people problems.
Word of God is that the accent is an early attempt at mimicking human speech that isn't quite perfected.
The T-800 asks for a plasma rifle at the gun store, which, obviously was unavailable back in 1984 or even now. But, it's entirely possible that in The Terminator's timeline, some sort of breakthrough was made in the field of plasma technology, but SkyNet's incomplete pre-Judgement Day records don't specify exactly how far along the research is. The Terminator was probably just taking a chance to see was it available.
As a corollary to that, The Terminator is likely well aware of what weapons could damage or destroy it, thanks to whatever data SkyNet has from years of conflict. In checking for plasma rifles, the T-800 is seeing what can be used against it and planning accordingly.
A common debate within the community is why Skynet doesn't just put a nuclear payload inside a fleshy covering and destroys all of Los Angeles and Sarah in one fell swoop. However, as an intelligence trusted to run the defense network, Skynet likely has access to government files and knows that it only exists because a T-800 from a future version of itself got reverse-engineered. Therefore, to ensure its own existence, it's not enough to just kill Sarah Connor, it also has to leave a salvageable piece of itself behind as well. Destroying the entire city its target is in would just be a mutual kill, which offers no benefit to a machine that can't feel spite.
Alternatively, nuking an entire city is sure to trigger an early nuclear war, which will ruin the world before Skynet could even be built.
Sarah called her mother against Kyle's advice, not knowing that the Terminator had already killed her, and gave it enough info that it tracked her down again. Taken in the context of the movie itself, she started the chain of events that resulted in Kyle's death in motion. In context of the franchise as a whole, Skynet might not have existed since Cyberdyne wouldn't have obtained the Terminator's CPU.
It gets even worse when you take into account the delete scenes for the film. We see Reese making pipe bombs in the theatrical edit, but we are never given any context for why, with the audience figuring they're being made to use against the Terminator if the situation calls for it. However, in the deleted scenes, we find out that Sarah looked up Cyberdyne Systems' address and pushed Reese into trying to destroy Cyberdyne before it could create Skynet (similarly to how Skynet had sent the Terminator back in time to try to kill Sarah before John could be born). The plan for Reese was to protect Sarah, not to try to destroy Skynet before it existed. With the delete scenes included, the moment she convinced him to attack Cyberdyne (which they were going to use the pipe bombs for), he was practically a dead man. It also explains why Sarah and Reese just so happened to find the warehouse that belong to Cyberdyne Systems: it's because Sarah knew the address and they were planning to head there anyway to destroy it before the T-800 showed up at the Motel and started the chase, and they inadvertently lead to Cyberdyne getting their hands on the tech that made the Terminator possible.
