I previously had the same setup as you...old computer an strava on phone in my pocket. When I got my second bike, I actually opted not to get Garmin or similar as it was too expensive after getting my new bike (maybe sometime in the future).

I use my iPhone but I don't mount it on the handlebar or use the display, instead I use the Wahoo RFLKT+ with the Wahoo RPM cadence sensor and Wahoo heart rate monitor. The RFLKT acts as the display on my handlebar, and the iphone GPS with the screen off gets much better battery life (i keep it safely hidden away). The only thing I would probably do different is get the speed and cadence sensor for those rare times where GPS signal gets weak as it might give me better speed output on the display. All this will work with Strava, but I like the way the Wahoo fitness app works with the RFLKT better, and it only takes a few seconds to share it to strava after my workout. You can also get the base RFLKT, but I wanted the altimeter and temperature of the RFLKT+ (also as an ANT bridge that I haven't tried yet).

Another suggestion is to look at the Cateye Stealth 50 GPS bike computer - it will do everything you want with ANT and much cheaper than the Garmin. Another option is the Sigma ROX 10.0, which is between the Cateye and Garmin in price and generally features.