How should a Traveler Pray behind a resident Imam, Shorten or Full and Vice Versa? – Assim Al Hakeem

I just have a question in regards to prayer. Alhamdulillah my iman has now peaked where i make niyyah that my house is a musallah, am I still required to go to the mosque for the obligatory prayers or is it sufficient I pray at home. By praying at home, I also make niyyah that I have energy to read quran later in the day, energy that I wouldnt have if I had gone to the mosque.