Almost everywhere we go, an article mentions how you shouldn't dive head-strong into any new (or old) crypto just because someone on the internet said you should, do your own research and find what fits your criteria. The thing in this advice is... most people can't really research in the manner these articles speak of. Most people also don't have criteria besides "if it go up, I rich", so researching isn't as simple as just searching something on google or looking for "the best new coin to invest into right now noW NOW!!!".
So how does one research coins and find gems and projects that may interest them. That's what I'd like to talk about, so let's start with the basics.
When looking at a particular coin that maybe someone pitched to you or you found on your own, look at the problem that coin is addressing and also search for why it might be important to solve this problem.

The immediate next thing to look at is, what is their proposed solution? Are there other coins trying to solve the same thing? Is the blockchain even the correct thing to be using to solve this type of problem?... Those are just some of the questions but one that I always like to look at the most is... Do I understand this project and does it make me feel comfortable to read about it and possibly invest. This isn't really advice in a sense but I find it much easier to invest in things I understand more thoroughly and things that are not sketchy or vaguely described.
The third part would be Tokenomics... but with many investors, looking at Market Cap, how new coins are created and if there is a max number of coins... doesn't really tell us anything. So while I wouldn't say skip this part if you do not understand it, skim over it at the very least cause there are always obvious signs of a failure if it is one.
Fourth would be the team behind the coin. Are they famouns/infamous? Do they have any other successful endeavors that would let you know if they are or aren't trustworthy? Do they have a realistic roadmap and do they admit their faults and cons?... There is a lot here to be looked at but it is all in essence to see whether or not you trust these people and if they have shown reason for you to trust them.

Then there is the market. Is the coin on any exchange? Why would people buy it? Is there any competition that is also just getting going or do they have to beat a competitor... Not much to say here, honestly speaking this part is something you look into at the very start and if the project has a large competitor the gamble will be significantly larger than if the coin was a one-of-a-kind thing.

And last but not least would be their website, social media accounts, general activity and responsiveness. Through these you can see the team and how they react to questions and whether or not they are critical of themselves and attempt to fix their mistakes.

There are always a plethora of others things you can check out with a coin but if you like a coin a lot, than checking all of these out can maybe ease your senses on how possible the project is as far as it's goals go.
I hope you enjoyed reading, this was just my view on researching crypto and what you might want to look at. Other people might not want you looking at any of these or they have their own system but this is mine and it comes in handy so go forth and invest my friends!