What was the time difference between video rental and video purchase?

slightly OT, but buying Terminator 2 on VHS in about 1995 is what caused me to loose faith in shopkeepers

went to the video rental shop

"can I buy Terminator 2 (on VHS)"
shop keeper guy looks at me and says
"hmm...what do you reckon...a tenner?"

from then on, I knew shop keepers make it up as they go along (I bought it for a tenner)

It was originally like that in late 70s when VHS rental places popped up. The tapes were very expensive and so people only rented them. But by the late 80s/early 90s they were available for sale inexpensively a relatively short time after the movie stopped playing at the theater. I remember my dad commenting about how the grocery store had piles of the Batman movie when the tapes were released.

I belonged to a few video stores and my friend's sibling owned a few stores. Studios priced the videos around $60+ each to be sold exclusively to video stores for renting. You could rent them for a few dollars for 3 days. After that, they would charge a late fee. Cheaper priced videos for consumers went on sale around 6+ months later after theatrical release. Movie channel release was likely in-between the two, but I didn't have cable at that time.

Netflix killed the video store. Returning videos so quickly was a hassle and late fees were common. But, Netflix would mail DVDs to the customer and never charge a late fee. When the DVDs were mailed back, you could rent new ones. Streaming put the final nail in video stores' coffin.

I remember when consumer DVDs began to be released only 3 months after the theatrical release. Great idea especially for blockbuster movie DVDs with a large fan base.

"I heard that when VHS was king, the video store would have it out before you could buy it."

For many years during the "VHS was king" period of time, there was no realistic option to buy it. You could technically buy it if you really wanted to, but it would cost you about $80 to $90 in early/mid 1980s money.

Top Gun (1986) was one of the first, if not the first, major Hollywood movies that was "priced for retail" rather than "priced for rental;" it sold for around $25 and pretty much kickstarted the entire concept of ordinary consumers buying movies. At that time they made up the difference by featuring a Pepsi commercial on the beginning of the tape.

"Then when DVDs came out, they changed this so you could either buy it at the same time or pretty soon after. This is one of the main problems that contributed to the decline of the video store."

That never changed. Video rental stores always got copies about a week or two before they were available for retail sale, regardless of whether it was during the "priced for retail" VHS era or DVD era. People who have experience with downloading bootleg DVD rips, starting in the late 1990s, know that the bootleg DVD rips were available online about a week or two before the same titles hit the store shelves (and even slightly before they hit the rental shelves), and that's because the major pirates like "aXXo" had video rental store connections.

There were a few times I remember the video being available for rent but not for purchase or if you wanted to purchase it, it was some crazy amount.

I believe the first Punisher movie was like that - you either rented it, paid $100.00 for it or learned how to work two VCRs together and made your own copy.