There may be multiple issues.
You mentioned Windows 3.11. As I recall, there can be some issues with Win 3.1 (which I've used) on systems with too much RAM. 256MB is okay. More than that can be iffy. In particular, I seem to recall needing to edit a configuration file, possibly just for installing Internet Explorer. When I was looking for a new system, quite a while ago, I recall documenting some RAM Limits I found, which will affect DOS, Windows 3.x, and newer Windows versions. I recall that some of the workarounds mentioned there didn't work real well.
HIMEM.SYS might want no more than 64MB of memory. That can often be worked around by using the /EISA switch, but, even still, MS KB 116256 mentions not being able to report more than 4GB of memory. So, yeah, I imagine that your 8GB laptop may encounter some issues.
You may need to adjust the "system startup" settings. (By this, I'm thinking of BIOS settings. However, newer systems may use UEFI.) In particular, SATA drives may need to use IDE/Legacy mode. Also look for Legacy/ISA settings in sections related to IRQs/PnP. DOS is really designed to work with BIOS, so a BIOS system may be more preferable than (U)EFI.
If your hard drive is too large, that may cause some issues. Anything that is 127.5GB or more will require LBA48 which isn't supported by these operating systems. If you apply newer patches (like those made by third parties, designed for Win98/ME), I think you could potentially be fine using a drive as large as 4TB, but of course you won't be using that much for DOS. DOS will want to only be using partitions under 2GB each, unless you're using a DOS variation that supports FAT32. (In general, as long as you're not violating important limits like the limit on a drive's size, DOS won't care how big your non-DOS partitions are, or the extended partition. Since this question is about the topic of newer hardware, I'm not referring to old limits related to things like outdated BIOS chips.) I do suggest placing DOS partitions first on the hard drive, as other operating systems are often better at loading from later parts of the hard drive. Each FAT32 is best to keep at some at 133,693,376 KB (slightly under 127.5 GB).
DOS FDisk may not like drives that are too large. Expect trouble if using a drive that is over 64GB, unless you use the FDISK from the downloadable update at MS KB Q263044. Even then, expect trouble that is cosmetic (for FDISK and FORMAT), but things will actually work fine. Alternative: use third party software (like XFDISK, or Ranish Partition Manager).
Other hardware problems are not too likely. In other words: I don't anticipate DOS being likely to break your hardware. However, hardware being completely unsupported is quite likely. USB may not be supported. You might be able to use a USB keyboard; that may require setting some sort of Legacy/Compatibility option in BIOS. Same comments can be made about a USB mouse; I would suggest trying a newer mouse driver (CuteMouse comes to mind). For other USB devices, including memory sticks, you may have some luck by adding some drivers/software that has been made well after DOS has been discontinued. I suggest becoming familiar with the FreeDOS website. (Besides distributing FreeDOS, the website also mentions lots of newer drivers/software that work fine with MS-DOS. The site has highlighted new software releases in a News section, but also lots of software buried in sections under FreeDOS software area.)
I've had troubles running XFDisk on a friend's system that used a 64-bit CPU. I suggest trying to boot DOS off of removable media before spending a lot of time trying to re-partition and install DOS onto the hardware.
In general, DOS doesn't know/care about the concept of hardware being virtualized. You may find that some of your real hardware may work easier when using DOS directly, compared to trying to get it to work in a virtual machine. The biggest exception to that might be USB keyboard/mouse, which some "virtual machine" software might emulate in a way that works nicer than the real things.
Some of the MDGx Windows 98 + ME •still• alive Campaign may also point to some newer resources, which may be helpful for trying to do newer activities (like using newer hardware) with this older operating system.
For games, many DOS programs were designed for sound cards that may not work as well on newer systems. Even if your system was a desktop, the lack of ISA support will rule out "Gravis UltraSound" and many other classic cards. You might, or might not, be able to get "Sound Blaster" support. If so, consider yourself lucky. Naturally, the fact that your system runs fast may cause some software to be unhappy. Software which might be particularly prone to such problems may be games, multimedia (media players), and maybe communications. Software which simply works with keyboards and hard drives will probably not be too unhappy about the unfathomable speed.