So... there's little in the way of established guidelines for those of us that aren't interested in having their group start at level 1. I know I'm tired of it and so is my group. My first instinct is to say that a 5th level character will have something like 2-3 common, 1-2 uncommon and 0-1 rare items at start, with [no clue at all] worth of coins left over... but that's just me.
On this, at least, the DMG provides some guidance. Page 38, at the bottom, has a table with suggestions for starting gear dependent on level and how common you want magic to be in your campaign. Compared to the number of rolls for treasure hoards suggested elsewhere in the book and your gut assessment, the numbers look low at a glance (in a 'high magic' campaign between 5th and 10th level, it suggests starting characters with one uncommon item, and that's it), but keep in mind the tables contain plenty of consumables, and the result of any one roll is getting distributed among characters in the party, plus it's for starting characters. While you're by no means obligated to go with that, it's a starting point.
As an alternative on the mundane wealth side, before the DMG came out my first instinct was to keep the starting kits but additionally allow players starting at sufficiently high level (like... 5+ or whatever) to get better starting items with their kits if they're proficient - for example, martial classes might get to start with a silvered weapon, someone proficient with heavy armor could start with splint or plate instead of chain, a mountain dwarf whose class wouldn't otherwise start with medium armor could start with half plate.
I don't mind their design philosophy to make characters less reliant on relevant gear to stay close to the power curve (I actually appreciate it in a vacuum), it's more the fact that since I have no practical expertise running 5th ed, I can't accurately gauge beforehand how much gear a party can have before they're ahead of the power curve instead of in line with it.
This interested me, so I took a quick look at the table for monster specs by challenge rating, under the creating monsters section. The easiest to eyeball is AC, where, with one exception, the value is at all times 2 below the average attack roll of a proficient character, of level equal to the challenge rating, starting with a 16 or 17 in their attacking stat and raising it at every opportunity up to its cap (i.e. the highest starting stat you can get with point buy or an array). Most importantly, there aren't any unexplained jumps (at level 10, it jumps from 16 to 17 one level later than expected), which tells me the stats indeed aren't assuming a numerical bonus from magic items - if you get one, it's purely a bonus, not a necessity. Save DCs behave similarly, though they keep scaling with monster proficiency bonus after 20.
If you want to be conservative until you get a better feel for the system, my suggestions:
-Magic weapons seem to be the closest to a necessary item, since a lot of creatures resist or are immune to (lycanthropes) damage from nonmagical weapons. However, a lot of these creatures are also vulnerable to silver weapons, which are much easier to get by, so if you feel handing out magic weapons to your martial characters at the earliest opportunity would be too conspicious, you can try subtly or not so subtly nudging them towards investing in silver weapons.
-Lean towards things that give the PCs more options over things that add bonuses to options they already have. Staves, magic wands, and rods are good for this, as are a lot of miscellaneous wondrous items.
-Consumables, such as potions or a necklace of fireballs. These can fall under the above, be added on their own merit, or act as a way to test what effect something will have on encounters. If you misjudge a potion, the worst it can do is make problems once, and then it's spent and you know better.
-General utility items. I've yet to see a player who'd say no to a good old bag of holding. The lack of WBL provides some freedom here, since in 3.5 these usually got ignored unless they were a really good deal, because that money could have instead gone to buying a more directly powerful item.
-My gut feeling about items that do provide a flat numerical bonus is they shouldn't be too bad individually. The main thing to be cautious of is stacking multiple bonuses, say cloak of resistance+ring of protection+ioun stone of resistance. The good news is a lot of these require attunement, and you can't be attuned to more than three items.
-If you have players whose bonuses are behind the curve for some reason, say because they went with a race/class combination that isn't 100% optimal or they spread their ability scores thin, you could target items that give bonuses at those players to shore them up rather than as a bonus.
-Keep in mind magical weapons don't have to give a flat bonus to hit and damage to count as magical - e.g. the Flame Tongue doesn't. Just giving it a cool effect is acceptable.
