My new Acer Aspire 7 doesn't have a Legacy Boot option, what can I do to get it?

In some BIOS settings (and if I recall correctly that was the case in several Acer Aspire models I have seen) the option was there under a different name: It was listed as an option to UEFI under the name CSM.

If it really isn't there at all (which wouldn't surprise me for an Acer computer as they are really focused on the low-cost Windows-only market) you will have to install the Linux in UEFI mode, but that shouldn't be a problem at all. Any reasonably modern Linux supports it, except some specialist distros designed to give elderly computers a second life. (These can be 32-bit only or use a V2 kernel and that won't work with a regular UEFI BIOS.)

In case your Linux distro of choice only offers a non-UEFI installation, it can often be easily made UEFI capable by downloading the ISO and using Rufus (or a similar utility) to write it to a USB stick in UEFI/MBR compatibility mode.

Be advised that using an UEFI system in Legacy or CSM mode is not recommended. The option is provided as a fallback, but your system will boot faster in pure UEFI mode. And in some cases not all on-board hardware can be utilized to its full capacity in Legacy/CSM mode.

I install Linux distros in such a way, that they are compatible with UEFI Boot (if a particular distro allows for this option, of course) or,

Most modern distributions support UEFI, both for the installer and for the installed system.

Technically, all x86_64 distros allow the installed system to boot using UEFI, some just need more work than others. At worst, if the distro doesn't offer this option at install time (let's say you're installing it using another PC), the manual process should be the same as it is for Arch:

1. During installation, make sure to create a small-ish EFI system partition.
2. Format that partition with FAT32.
3. Install an UEFI-capable bootloader such as GRUB2 or systemd-boot into that partition.
4. If the bootloader's installer hasn't done so, copy its *.efi file to EFI/Boot/bootx64.efi.
   (When installing GRUB2 this can be done using grub-install --removable.)

Step 4 is most important here; it's the primary difference between installing to removable media and fixed disks – because you cannot carry NVRAM variables with the USB stick, UEFI offers an alternative option that relies only on a specific file path. (This is how the distro installers themselves boot in UEFI mode.)