Welcome, Mike.
Last I checked the Jose kit was around $1500 or so, but that was a few years ago. You’ll need to choose an engine and gearbox, which are relatively inexpensive compared to a V8. The big advantage is that the V6 kit is much less intrusive to the body of the car. In order to shoehorn a V8 in its lots of bodywork to the tunnel and front suspension. Always buy the best donor car you can, with as few missing pieces as possible. Decent Alpine Series V donors are available… keep your eyes on craigslist.
The sky is the limit of course. Since you are doing your own work you’ve got a huge cost advantage. The standard 1725 engine is no slouch if properly tuned and prepared, but the V6 has advantages over a proper Tiger as well.
Reference this earlier post:
https://www.teae.org/cars/forum/viewtopic.php?f=4&t=1131
Here’s a newsletter article from Rootes Review by Gary Schotland:
http://www.team.net/www/rootes/sunbeam/alpine/mk1-5/techtips/alpv6txt.html