Could you please tell me if the modals I have chosen are correct or are there other possibilities?
If the initial capital "I" is the pronoun, that would be incorrect with the verb "were". Both of your choices could be used here, but neither should be used with "regularly". That combination is redundant.I/ We were beginning to get more and more fed up with the “holiday by the sea”. We (modal + go + always) 1 WOULD ALWAYS GO / ALWAYS USED TO GO (both?) to the south coast regularly for a fortnight every summer.
2. There was "no chance" would be better.There (not + be) 2 WAS NOT a chance to have a proper summer holiday last year, so we (decide) 3 DECIDED we (modal + have) 4 SHOULD / WOULD / MIGHT / COULD (?) HAVE some sort of a winter holiday.
4. should/would/could (not might, IMO)
6. would/mightSome friends of ours (tell) 5 TOLD us we (modal + not + enjoy) 6 WOULD NOT ENJOY a skiing holiday, that it was always so cold you (modal + go) 7 WOULD / MIGHT GO skiing just to keep warm.
8. yesWe only (have) 8 HAD eight days instead of our normal fortnight away. All together, with the return flight, accommodation, etc., it (come) 9 CAME to about £125 for the three of us. And it was worth every penny. I mean, I work hard all the year round. I (need) 10 NEED a complete change
11. was willing (but that's not a modal)and I (will) 11 AM WILLING to pay for it. I (modal + recommend + certainly) 12 WOULD / SHOULD (?) CERTAINLY RECOMMEND a holiday like this to anyone. We saved up for it, by the way, by cutting down on luxuries.
13. would/willII/ If you (modal + take) 13 WOULD TAKE (is SHOULD TAKE possible?) a seat, the doctor (see) 14 WILL SEE you in five minutes.