Typically the dead giveaways to a cheaper kit is the spring on the strainer. You want a nice tight spring. Think this:

https://www.amazon.com/Professional-Hawthorne-Cocktail-Strainer-Mixologists/dp/B08BKLPC36/ref=sr_1_3_sspa?crid=36TUJV7YPWD49&keywords=cocktail+strainer&qid=1676505718&s=home-garden&sprefix=cocktail+strainer%2Cgarden%2C159&sr=1-3-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUE3U0dLUTA5T1VYUUsmZW5jcnlwdGVkSWQ9QTA2Njc3NjUyVE9VVTkyWDU5NVZMJmVuY3J5cHRlZEFkSWQ9QTA0NjYzMjgyVVAyR1hFMjQ2S1gzJndpZGdldE5hbWU9c3BfYXRmJmFjdGlvbj1jbGlja1JlZGlyZWN0JmRvTm90TG9nQ2xpY2s9dHJ1ZQ==

vs. this:

https://www.amazon.com/American-Metalcraft-S209-Stainless-Cocktail/dp/B0077E1NVC/ref=sr_1_6?crid=36TUJV7YPWD49&keywords=cocktail+strainer&qid=1676505718&s=home-garden&sprefix=cocktail+strainer%2Cgarden%2C159&sr=1-6

Also, the two piece soldered jigger is suss. Also a longer spoon is nice.

It's all serviceable stuff, but if your going to be making cocktails often then I would suggest just buying items individually as you can afford them. Start with some really good weighted shakers and then just build from there.

Not that there are any rules.