The Collectors Edition ("Gold") is Windows native and, thus, wont run in DOS.
The TFTD Extender program runs on the Windows version, providing a mouse-resizable window, a smoother-running, more responsive screen than DOSBox, and a host of fixes for various bugs or exploits in the game.. It also supports the use of higher-quality .mp3 music from the PlayStation release, and keyboard shortcuts. XcomUtil provides bug fixes, including for the disjointed-base bug, and additional ease-of-use features like the automatic re-equipping of soldiers before a mission and appending rank and stat info to soldier names.
Both also offer many gameplay modifications such as enhanced weaponry, different starting-base layouts, and randomized terrain and UFO layouts. These are all optional and turned off by default.
The programs are confirmed to run on Windows 7 as well as older operating systems, and with the Steam release.
XcomUtil supports the TFTDExtender launcher, but assumes the use of DOS or DOSBox at several points in the installation process, so specific steps are required to run them simultaneously:
DOS/32A is a more advanced extender and open source replacement to DOS4GW. It can improve both performance and stability of X-COM.
To improve DOSBox performance make the following changes to the DOSBox configuration file:
cycles=auto limit 10000
UFOPedia has an excellent article on this here.
The Research tree bugs can generally be fixed by using TFTDExtender of XcomUtil. If you are reluctant to use these you could try the TRTBAG instead.
Some digital versions of CE shipped without their MIDI sheet. Copy these into the sound\ directory.