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I'd generally stay away from i3, but it's better than nothing, and I would definitely go with Lenovo as the brand - excellent experience with them and my brothers have never had any issues with them either.

So, I'm not sure if this is a viable option for the use case as it would take some getting used to. But have you considered possibly getting a chromebook? It may sound crazy, but you can get a pretty decent chromebook for relatively cheap, and within the 349 US price range.

The big problem with that would be getting used to the chromebook. Chromebooks, running on chromeos, have different features to windows, and have more 'limited' capabilities. However, depending on the specific use case (from what I gather is: web browsing, and writing/ editing documents), a chromebook would be perfect.

The big change would be switching to google docs as the main editor over word. Yes, google docs is limited on some features, but I still found the transition quite smooth personally. In terms of functions and uses, I would say the switch between google docs, and MS word is seamless, with majority of the controls being in the same places.

If your father needs the documents to be in MS Word format (i.e. docx), then google docs does have an 'export as MS Word' option for saving the file.

The big thing to think about here though, is internet, chromebooks are basically useless without it, so it depends on whether your father has access to the internet every time he is using the device, or if it is periodic. (although you can enable 'offline editing for google docs').

In terms of longevity. I have an old Acer C720 chromebook, which I have had, and used daily for just under 7 years now. (I had the 'EOL' update about 4-5 months ago, and google retires devices after exactly 6.5 years). In fact I am currently writing this response on said chromebook, and I don't find it slowing down too much even now. The newer models of chromebooks that are avaliable right now have better specs than the c720, so I would assume that longevity (without slowing down) would be even better.

Sorry for the huge wall of text, but I just wanted to get everything down, for the main points to think about. But from what I can tell, a chromebook may be a good bet, if your father would be ok with switching/ getting used to chromeOS.

Celeron N3350
ooO(...)
Core i3 8145U
ooO(8)
Core i3 1005G1
ooO(10)

Intel Core i3-8145U @ 2.10GHz vs Intel Core i3-1005G1 @ 1.20GHz [cpubenchmark.net] by PassMark Software
https://www.cpubenchmark.net/compare/Intel-Core-i3-8145U-vs-Intel-Core-i3-1005G1/3349vs3560

HP win :D

Sorry I'm no good at computer hardware stuff. But like you I know the difficulty of parents using computers. My mom.would click on ads all the time and get tons of stuff inadvertently installed on her laptop. No matter your choice, I would recommend taking the time to install adblockers add-ons your father's browsers, it doesn't slow-down his laptop over time. For chrome browser, I use uBlock and Ad Blocker Plus. I whitelist this site, but many other sites can be really intrusive.

You may want to check older laptops or even used ones. For example this is around $240 and it has i5.
https://www.amazon.com/Lenovo-T430-LED-backlit-Certified-Refurbished/dp/B0733H5YZY

I think even Lenovo T410 may suffice, you can find it around $180 I believe. Used of course.

I was gonna recommend SSD upgrade with Linux but then realized it's for your father and already resigned that thought.

2 weeks ago my dad was complaining for the same thing, his computer was taking so long to do anything, indeed your situation is pretty close to mine, even your described specs are pretty similar. What I did was cleaning his PC inside (for dust) and I made a factory reset on the laptop. Now it looks almost as new. Still, if your dad doesn't mind spending money on a new one, from the ones listed above I would personally go for Lenovo, as Mayanaise as said it's an excellent brand and the one I'm currently typing on. Another solution and probably my favorite is to try doing a factory reset like I said before and I would try to gather some money overtime to get an i5. Hope that helps :)

For his uses, I'd almost say that the SSD upgrade might be enough. If the physical laptop is holding up well (hinges are operating well; body isn't cracked, warped, or deformed in any places; keyboard still works well; etc) the bump in speed could wait until that laptop is kaput. And if that investment holds him over for a couple of years, the next round or two of laptops in the low end price range are looking to be a promising bump in casual computing. Better battery life, fewer CPU compromises, and stronger GPU cores (which are useful for accelerating media playback and, surprisingly, web browsing.). I've personally been recommending that family hold of on laptop replacements where possible. After an SSD upgrade, most are fast enough.

But if you really want to get him onto a new laptop, I'd go with the cheaper one. The ram is more useful if you're certain the 128gb is enough storage. The 16 GB Optane will be of little use to him. I'd also recommend considering choosing the lower resolution screen. He doesn't sound like much of a multitasker, and the lower native resolution will produce larger fonts at the proper aspect ratio for easier viewing. If his eyes don't need it now, they may appreciate it over the next 3-5 years.

The only concern I have with a laptop intel processor ending with a u is that the that ultra-low power series of chip will throttle if it gets hot. This may not be a concern now, but it might be in a few years as programs (not to mention windows!) get bigger and beefier. A trend I have noticed is that as technology advances, so does program size and requirements. For example: several years ago my XP could no longer run the newer versions of Chrome, despite having used it for years. The new version of that browser was too memory hungry to run on that PC.

I also have never heard of a processor ending in a G or the octane thing.

The HP laptop does have a faster CPU (and more RAM+SSD), but not by much. A good website to check CPU performance is notebookcheck.net, they usually show the results of various benchmarking utilities for laptop CPUs. You can see the scores for both processors here:

https://www.notebookcheck.net/Intel-Core-i3-8145U-SoC-Whiskey-Lake.321348.0.html
https://www.notebookcheck.net/Intel-Core-i3-1005G1-Laptop-Processor-Ice-Lake.423869.0.html

Intel Optane doesn't really help in home use, especially if you have an SSD. Its purpose is to act as a very fast SSD or RAM in order to speed up certain types of applications, but if all your dad is doing is Microsoft Office work and general internet browsing, it won't be of any real help to him.

More RAM is definitely a good thing, especially if he's intending to keep the laptop for a few years in the future. However for Office and general internet stuff, 4GB is enough. You can always add an additional 4GB stick in the future for ~$30 and get 8GB in total, if you find that he needs it. Since you've also mentioned in, SDRAM is just the technical name for memory modules that computers use, every RAM is SDRAM.

If money is critical, get the Lenovo and upgrade the RAM in the future. It's still much better than any Celeron laptop and will be for several years. The HP laptop is faster but not by a significant amount, you're mostly paying for more RAM and SSD, and you said 128GB is enough so there's even less point to pay extra.