Welcome and, great questions and great answers. let me add a few cents worth.
1. I drive a Midget and am 6', 250 lb - yes I wear the car a bit but, size is not a problem. However, the car size kind of is - Midget is a 50 mile car. I love it but it is not a car to go for a long drive in, it is a car to go for ice cream in.
2. Start with what you want. Not sure how old you are but, assuming you are of a similar vintage to then rest of us time ain't exactly on our side and restoring a car never ever takes less time than we budgeted. Again, I love my Midget and it followed me home but, I might not have chosen it had I had all the classifieds open in front of me.
3. An expensive car (mostly) doesn't cost a lot more to restore than an inexpensive one. Somewhere on the interweb Jay Leno discusses this - body work is body work, paint is paint, and with LBCs even many of the internals are common.
4. 25k is a very good budget for most British cars. Decide if you want to wrench or if you want to drive and buy accordingly. The garages of the world are full of cars people bought to restore only to discover they really just wanted to drive. - your budget will get you a very good TR6/ MGA/ TR4/ not likely a big Healey but, even there, if you wait. Also, depending on your tastes (I note that you like a 60's look) there is Jag XK8s for peanuts, and the XJS is looking prettier and prettier by the day. Not strictly 60's but the price is great, it has cruise control/ AC and you could drive anywhere in the country. (I have a guy in my club who drives a Stag - but swears by his XK8 - 30 mpg and very comfortable.)
5. If you are committed to an older car, you might also consider some slightly more obscure cars, Triumph Stag/ Jensen Healey/ MGBGT/ even a Jensen - I think they are mostly undervalued and parts are still rather available.
6. LBC's are like buses - there is always another one coming. You might want to join a club as I think club members are typically far more realistic about the value of their cars than the general population. (Note - just took a look at the Idaho club classifieds and you can get a Singer for half a similar MG -
https://www.idahobritishcars.org/links/?listing_order=year&listing_orderby=ASC
7. Good luck and this is a great place to hang out both for advice and for fun - keep us posted!
cheers
JP