LTspice is the de facto standard for free SPICE-compatible simulators, and it's the most advanced in both engine and interface. Has a big community and very long history, which means thousands and thousands of component models from all the manufacturers (outside the ones from the default LTspice libraries and LTspice examples), and you can easily find answers/tutorials/examples, etc. about how to use LTspice, from the most basics to the most trickiest simulations.
TINA-TI only makes sense if you must use particular TI components that only have TINA-TI models that can not be ported to SPICE. I've tried TINA-TI a couple of years ago, and found it cumbersome and slow. And close to no online usable answers when you search for anything else more complicated than basic usage.
I will recommend LTspice without hesitation, for either beginners or advanced users.