That’s a super plan: realistic, affordable, keeps all your options open.
Don’t apologize for looking for help- it is the raison d’être of these forums! You have a lot of very experienced posters on here, who really are here to pay it forward from the people who helped us along the way.
Take time to craft your list:
*UK- pros are (except for Oxbridge/LSE/Imperial/ maybe UCL) pretty predictable admissions, and decent potential to stay and get a work visa- talk to your parents about which unis they feel tick their prestige meter
*Canada- almost as predictable entry as the UK, and good potential to stay and get residency- again, talk to your parents on which unis they feel would be “worth it”
*US- Do your homework and ID programs that you would like and that fit in your budget. For programs that you like but that your parents might not realize are as good as they are (such as CalPoly SLO or Purdue) put together a pitch sheet: stats of incoming students, employment outcomes, companies that actively recruit there, rankings in engineering circles, resources available, etc. For the programs that they like but are improbable (such as MIT or Stanford) have them do the cost estimators on the websites.