I personally prefer a boot over trail runners for true backpacking. I'm 50+ y.o. and my ankles are worth (and need) the extra investment of weight and cost. I've always told folks that boots need to be purchased in a real store where you can try them on and test as mentioned previously (stand on an incline, kick your toes forward and backward - you shouldn't feel any pinching or tightness). But if you truly, really can't make it to a store, there are many online options available that help - free shipping & returns, etc. For my current boots (Zamberlan Vioz GTX) I broke my own advice and ordered on-line. If your credit card limit can afford the hit, order the size you think you'll need, then also the next half-size up. Try them both on at home with the socks you plan to wear (VERY important!) and just return the size you don't like. Having 2 to compare always makes a difference. I worked in an outdoor retailer all through college and we always looked for a thumb's width of room between the end of the boot and the end of your big toe. This gives room for your toes during descents. My Zamberlans are European sizing, so I traced my largest foot on a piece of paper and measured from end-of-heel to tip-of-big-toe for the right metric sizing. I also cross-checked that measurement with the retailer's on-line sizing chart and was able to get a great fit with my order. With a wide foot or even a high arch, try to find a boot with as many lacing points as possible so you can fine-tune the fit with the laces, even in a boot with a Wide size. I also advise to buy the best boot you can afford - 100% of your body + pack weight travels 100% of the miles on your 2 feet & boots. And don't forget to invest in good socks - cheap, ill-fitting socks can negate all your investment in a great pair of boots. I love my SmartWools and Point6 paired with CoolMax liners for heavy backpacking.
One of my sons wears Asolo TPS 520 and my other son likes his Lowa Renegades - both are GoreTex.
The Lowa's have several nylon or leather panels, which means extra stiching. Although the panels lighten the boot weight, all that extra stiching can sometimes become a point of failure. Best to read the online reviews and see if this is a concern. I personally prefer all leather, but I also recognize that I'm carrying extra weight. BTW, the Zamberlans are the most comfortable boot I've ever worn.