Please don't bother responding unless you've read the full post. You're wasting my time and I've dealt with enough of that for one lifetime.
I think my biggest problem with the AI LLMs that I've used is lack of attention to detail. They will say things that contradict previously established facts of the conversation. They bring up details irrelevant to what I've asked about just because they might be broadly related or commonly referenced in relation to the topic on other websites. They contradict things they or I said in previous messages without even acknowledging the contradiction. They'll sometimes present information as hard facts and their only references are comments on reddit, which obviously come from some random person who doesn't necessarily know what they're talking about. They'll sometimes have a reference that doesn't in any way support what they said, and then when asked for some kind of quote from that source that backs up their point, they can't do it. They won't caveat any information; they won't bother mentioning if they're uncertain on something and they won't bother asking for more info or stating that they don't have enough info to accurately answer the question and will instead just answer it anyway with incomplete info.
I don't necessarily need it to be quick or be able to handle complex coding or to be able to automate things or to be some heavy maintenance productive machine. I just want it to be correct and intelligent and rigorous in its logic. I just want correct information when I ask questions. Maybe those questions will be simple everyday life stuff or maybe I'll ask it to help me understand something from maths I struggled with and so I want it to be pretty intelligent too.
So I guess I'm asking if you either have suggestions, or could guide me into being able to find the best model by myself by telling me what AI parameters I should be looking for and where I can easily compare them for some popular models.
For reference, I've used Deepseek for the most part. Recently I started trying Claude Sonnet5.5 and ChatGPT Terra5.5. They are all kind of stupid, even on the maximum effort mode and DeepThink. Deepseek is probably the least bad of the three though. So I haven't tried a paid model yet, but I thought I'd ask before I'd start to. Budget of maybe $30/month USD. Not willing to do self-hosting or whatever, I just want something I can have on the browser or download an app for.