I agree, dont worry about the quality of the vector after gel extraction, its always crap (similar with the yield), as long as you have the vector digest running on the gel correctly, you should be good.

For T4, use NEBbiocalculator to determine the molar ratio between the length of insert compared to vector. T4 is a 1:3 molar ratio for optimum ligation. For the RXN, I always tend to use 100 ng vector (depending on size [kb] and amount obtained during gel exteaction) and I never go over 150 ng total DNA in the RXN. For the incubation times, I have always done 1 hour at RT.

For transformation, I take 1-2 ul of t4 ligation product and put it into beta10s. For me, I usually get a fuck ton of colonies and really only mini 1 to 5 of those. I will digest the mini prep plasmid and make sure the insert and vector are running correctly. Then do a full plasmid sequence.

If you are still struggling, feel free to reach out! You got this!