Some things to think about:
Resolution: 3 1/2 digits (counts to 1999 or 3999) are common, 4 1/2 digit will add a bit of a price jump. More than that and you're talking expensive bench type meter. What do you need?
Range is how those counts are used. 199.9 mV , 1.999, 19.99, 199.9 volts full scale. That's four ranges there.
With some meters, you have to select the range, others will autoscale to the correct range.
Ability to measure AC and DC voltage would be eight ranges (four of each). Adding AC & DC current will bring your total to 16 ranges.
Resistance measurement will add another set of ranges to your total.
That's the basics. Then you can get into some more elegant or specialized measurements.
True RMS voltage and current will add a pretty good price jump. Personally, I think it's well worth it.
Other functions you may want: frequency, capacitance, inductance, temperature measurements, transistor checker; all will cost you. Some more than others.
And keep in mind that generally, any meter that can make lots and lots of types of measurements may not be able to do all of them well. A frequency counter will generally have better range, resolution and accuracy than a 3 and a half digit multimeter on its frequency setting.
Some meters (Fluke for one) include measuring seimens. (The inverse of resistance. Useful to measure the quality of insulating materials.) Some meters may have extra high or low range measurements. For example, most hand held meters have resistance ranges that can measure with a resolution down to 0.1 ohm, or up to 20 megaOhms or so (but not at the same time). Do you need to measure much lower than that, or much higher? That will add cost.
Some meters also allow you to log measurements. For example, make a voltage measurement every 10 seconds and store a couple hundred readings that you can recall later. This also costs. Some meters allow a computer interface.
So, think about what you want, need, and can afford. Go to the website of some distributors or manufacturers and see what's available. (DigiKey or Active Electronics as example distributors, Fluke, HP, Tektronix and others make meters.)