The HP 3468A/B is sometimes substantially cheaper than the 3478A, but with almost identical features (the 3478A has GPIB, one lower DCV/R range and slightly better accuracy). The lack of zero function and the non-backlit reflective display with poor viewing angle are the main downsides in my opinion.
If you don't mind the size, the HP 3455a, 3456a and 3457a are well regarded. Only the 3457a has current measurement ranges, but the 3455a and 3456a have LED displays that are much nicer to read than those annoying unbacklit LCDs. Calibration would be expensive since these require manual trimmer adjustment, requiring a calibration tech to do actual work beyond hooking it up to a calibrator and pressing start.
Many of the older bench meters (before late eighties models) lack convenience features like diode test and continuity. Note that ACV/ACI was optional on the Fluke 8840/8842, and that the options check marks on the back are not always accurate. Other interesting models may be the Keithley 199/196. The 199 has similar features as the Fluke 8840/8842 and HP 3468a/3478a. It does have a zero function, and a large high-contrast LED display. You can sometimes find them for well under $100. The 196 has more features, is 6.5 digits, but rarer and often more expensive. The HP/Agilent 34401a is from a later generation with more features. A very similar instrument is the Keithley 2000. Both have nice VFDs that provide good contrast if they didn't get dim from being turned on 24/7 for many years. Finding them for under $300 might be hard, especially if you want calibration included.
Newer instruments are often cheaper to calibrate, but more digits tends to be more expensive since it requires more expensive equipment. Be careful with meters sold with calibration certificate. Unless the calibration is performed before shipment, the certificate may be old by the time the instrument gets sold. If the calibration is not traceable to national standards labs and performed to factory specs, then they may have used any old calibrator and twiddled some knobs to adjust the instrument to whatever voltage the calibrator put out. They should have no problem providing you with a sample certificate providing the equipment used for calibration, their serial numbers, and calibration dates.