Suggestions on Replacing My Inspiron 3847

That would be fine but if it is strictly for business use with no gaming then either the Precision , Vostro, or Optiplex line would also do well. Personally I lean toward Optiplex since they are very versatile if you decide to sell it some time down the road.

3847 is a standard mini tower.  17.32 x 6.89 x 14.45 inches

3910 is smaller: 11.54 x 6.06 x 12.77 inches

when I go to bestbuy to look at the new Dell inspiron desktop mini tower, it is truly not inspiring in chassis aesthetics.  seems too small although the components are new.  For someone used to the standard Dell minitower of the past, it may take some time to get comfortable with the new wimpy small chassis.  maybe it is advisable to go to a retail store to look at inspiron yourself to decide.

I did a quick check for you and I found the Inspiron 3910 starting price at $500 usd.  It comes with an i3 12th gen CPU, 8gb of memory, 256gb of ssd and base chassis 180w power supply.  Moving up to an i5 will cost you around $600 - $700, and an i7 configuration can reach 1 grand.  The build quality is basic, entry level performance regardless of which configuration you get.

I suggest to look at Dell Outlet site.  It offers significant discount during holidays, mark down some systems with very attractive pricing.  At current time, for the same investment you will make for a 3910, you can get an XPS 8950.  A base model will start at around $500 as well.  I will select this XPS 8950 configuration as an example:  Outlet Price $806.99

• Intel Core 12th Generation i5-12400 Processor (6 Core, Up to 4.40GHz, 18MB Cache, 65W)
• Windows 11 Pro
• 1TB PCIe M.2 NVMe Gen 4 Class 40 Solid State Drive
• 8GB (1X8GB) Up to 4800MHz DDR5 UDIMM Non-ECC
• 8X DVD+/-RW
• Killer Wi-Fi 6 1675 (2x2) 802.11ax Wireless and Bluetooth 5.2
  US English Keyboard
  Dell MS116 Optical Black Mouse
  750W Chassis with Optical drive (Night Sky Bezel)
  Power Cord 125V
  Standard Air Cooled Heatsink Solution

Some noted upgrades worth the price are in bold.  You can review other systems here.