> What's the best route to go so I can play?
Get a used PS2 and a copy of this game off of amazon (or whatever your version of an online retailer). Something like gameshark or freeMcboot is also nice to have. You will need some sort of memory card if you go this route
>Can this game still be purchased new and if it can be, where should I look?
Yes but it is becoming more rare.
Assuming you are in the US... https://www.amazon.com/Tokyo-Xtreme-Racer-3-PlayStation-2/dp/B0000E3D8T/ref=sr_1_1?crid=25J023QEUSE3H&dchild=1&keywords=tokyo+xtreme+racer+3&qid=1592593488&sprefix=tokyo+xtreme%2Caps%2C165&sr=8-1
-Where is the best place to buy a PS2 from?
Assuming you are in the US... https://www.amazon.com/s?k=ps2&ref=nb_sb_noss_2
You might be able to find cheaper prices in ebay, facebook sales, garage sales, gaming stores that sell used stuff, craigslist, ect...
-Is there a PlayStation store where a digital copy can be purchased from and played using a PS3 or PS4?
I wish... The devs were on the intial PS3/4 developers list but I have not seen any games from them outside of the PS2 or xb360. They might do Japan only games now but they haven't made another TXR game since their Japan only game for cell phones a few years back.
I heard rumors that the devs had issues with the music license so none of the games got re-released and it seems like no plans that I am aware of for years. I dont know if the rumor is BS or not so dont take this part as fact.
-Are there any emulators that come with this game?
I don't understand what you mean. You can get a PS2 emulator and an .iso of the game just like any other older console, but that is it for any emulators in relation to this series that I am aware of. Very simple to find with google. Plenty of youtube videos to get you started