LVT can be installed as a DIY project if you are up for that to reduce costs.

As either a DIY or contracted install, I wouldn't go with the cheapest as it would mean the thinnest wear layer, making it susceptible to quickly showing scratches, etc. A commercial grade LVT would have about a 28 mil wear layer and a higher end residential might be around 20 mil. Some are as thin as 2 mil and higher price does not always correlate to thicker wear layers.

JM$.02W

I bought both our LVTs for this price or cheaper and they were excellent quality (one was on a good sale, one was a remnant from a commercial grade install). The installation would not have been cheap and would be impossible to fit into a $2.25 budget if you wanted good LVT. We installed ours ourselves, and it was very simple to do.

You don't have a good budget to get anything installed honestly. I'm not sure what the install cost is on LVT or LVP, but I would guess its your entire budget.

Installation isn't bad if you're a DIYer.

We went with Coretec XL in Montrose oak for our basement. I'm in the middle of installing it myself. I like it a lot, but its more than your budget. I found it difficult to find anything with a decent wear layer under $3-4 psf. We found Floor and Decor had some in the high $2, but they seem to have mixed/no reviews.