Hi David
I can't really add a lot to what's been said, June is not the time for your first visit to Goa.
The time I like the best is mid Nov to end of Jan, Feb to April can be very hot and humid, at the moment it is 40+c.
Early morning and evenings are great but I stay in the shade for three plus hours from midday.
Coming to Goa for the first time I would look at getting a cheap package for a two star hotel in North Goa that you can move from if you do not like it or use as a base to explore from.
IMHO Goa is not a 5* sit by the pool type holiday, you can go anywhere in the world for that.
Goa is a place to unwind, a walk down the beach to find a shack you like the look of to relax, eat in or doss on their sunbeds for the day, a stroll down the road in the evening to find a place to eat some of the best food to be found anywhere at a price that won't break the bank or hire a taxi for the day to go on one of the tour reps recommended trips for half the price or just to explore further north or down south.
If none of that appeals how about a train to Hampi for a few days or a flight up to Delhi and the Taj Mahal
You just have to do it