Tire clearance is going to be key here. Today you really want to be able to fit 40+ tires in the frame with room to spare. I would say minimum for a gravel bike is 35-38 with room for debris on all sides. Most road bike frames you will find just will not have room for this.

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Some bikes will allow greater tire width if you drop down to 650b wheel size, but it just depends how they shaped their chainstays; some frames it doesn't really buy you any more space in the back.

You'd have a better shot using a MTB and converting it into a gravel bike. Most road bikes won't accommodate larger tire width.

Check https://gravelcyclist.com/...-monster-cross-bike/ for instance. I've seen the bike up close (and the rider, who is a good mate).
Accommodates pretty much anything you could throw tire wise.

As mentioned above, if you go with an old road frame clearance is going to be your concern. Some older CX bike do have max tire clearance in the 35-40 range. As for how much clearance/how wide of tire you need, it just depends on where you plan on riding. I’m able to get by just fine with 31-33 mm tires on the gravel/dirt roads I live by. Other people live near roads where they want something 40+ mm.

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Matt

Dan's front page article hits on a key point to consider. Throwing stupid big tires on a 700c wheel isn't a great approach so think about the kind of terrain you want to ride. If its mainly back roads with a little gravel stick with 700c wheels but if you want to hit the single track use a smaller wheel.

If you want to attack gnarly terrain on a budget I would buy an old cross country mountain bike with 26 in wheels and go Tomac style. This is an very cost effective way to build a gravel bike but you become limited on tire and wheel choices.

Alternatively I would buy an old cross bike and tweak it so its more suited for the road. Most cross bikes will accept at least a 38mm tire which as big as I would go on 700c wheel.

If we use Cannondale as an example the one bike I would NOT recommend is the alloy Topstone. Its a bike designed to be able to do everything in a below average way. It really feels like they designed the bike to hit the buzzwords but weren't bothered with how it road. The fact that they didn't apply their famous CAAD system or top end allow to the frame design is indicative of the bike being a second tier option in their line up. This isn't all that surprising given they already make a range of excellent gravel bikes. The Synapse has clearance for 35mm+ plus tires and works really well until things get rough and muddy. The Super X and CAADX take things up a level in off road performance and then the Carbon Topstone is available if want more mounting points at the cost of a bit of extra weight. Then if you really want something extreme you can get a Slate. For reference the Slate SE Apex is the same weight as the 105 Alloy Topstone but you get a suspension fork which gives an idea of how much extra weight is on the topstone frame.

The big thing is to sort of what you want from a gravel bike. That's going to depend on both you as a rider and what your local gravel is like.
If all your "gravel" is well-groomed velodrome-smooth hardpack dirt, a road bike with 23mm tires at 110PSI might be fine. But if there's a lot of double-track made made from really chunky aggregate, you'll probably want 40s or bigger. If you have lots of mud, you might want some spare clearance even if you aren't planning on using super-wide tires.
Think about what you expect from your drivetrain arrangement. How much steep climbing will you have to deal with? Will the gravel bike see a lot of paved miles, and how sensitive are you to gearing step size? Frames with cylindrical seat tubes usually allow you to mount just about any front derailleur at any height and angle; some frames can't mount front derailleurs at all.

From the late 1980s up until fairly recently, a high fraction of road bikes had very restrictive tire clearance, and are unlikely to make good gravel bikes. Cyclocross bikes from this era are often fine, but if you need a tire wider than the low-30s range, you'll still want to pay attention to the actual clearance.

Many road bikes from the early 1980s and before have fairly healthy tire clearance. Nearly all road bikes had healthy room for at least 30s, and a few can reach the upper 30s without flying too close to the sun. Right around 1980 there was also a beautiful time when the world was heavily dominated by 28.6mm seat tubes and 1" steerers and 68mm BSA bottom bracket shells, resulting in bikes that are still very easy to find compatible parts for today.
There are some caveats, though.
Road frames from back then were spaced narrower at the rear dropouts than today's bikes, so you'll want to re-space the frame if you'll be switching to a modern drivetrain with a freehub.
If you'll be doing a lot of interesting descending, brake choice can get tricky. Cantilevers and dual-pivot centerpulls can be tricky to set up, and their mechanical advantage tends to be low, but decent ones can feel pretty good if you manage a good setup. Single-pivot calipers, however, are usually both weak and spongy. If you want to replace them, you'd have to either modify the frame (tricky) or find a non-recessed-mount brake. There aren't a lot of modern options, although picking up older centerpull calipers on the cheap is definitely an option.

If you need really wide tires, old rigid mountain bikes can be a decent basis for a gravel bike.
The really early mountain bikes can be pretty convenient to work with, but initially had beach-cruiser-esque geometry. When postured and fit like a road bike, this can make for some moderately esoteric characteristics. Of particular note, the super-long chainstays can make it hard to weight and plant the rear wheel, and the high trail results in a lot of wheel flop, so they're not the most confident or lively bikes on steep climbs. And the difficulty of bringing weight off the front wheel can make them a bit unconfident on super-loose surfaces as well. Not to say that they can't be loads of fun, but... things to be aware of.
Getting more toward the NORBA era circa 1990, MTBs got somewhat more road-bike-shaped (and then later started getting longer and slacker in front again towards today). You could also look into 1990s hybrids, some of them were lively wide-tire 700c all-rounder frames that can take a drop-bar conversion just fine.

If you start with a 26er MTB, tire choices are growing scarcer, but there are still good options for all manner of surfaces. Obviously there are still lots of MTB and beach cruiser tires floating around. If you want a lively fat slick, Panaracer Pasela is a good budget choice, but I usually keep my '84 Stumpjumper fitted with Rat Trap Pass tires.

As always, remember that trying to save money by modifying a cheap bike can sneakily morph into an expensive route if you start getting creative and having too much fun. :)

The key here is all about tire clearance.

A road bike will likely be stiff. To combat that you need big tires at low pressure. Used endurance disc brake frames will likely get you into cx 33mm wheel territory. Might not be enough if you are big.

But if you really want comfort, or want to get into more intense gravel or even light singletrack (fun), then you want geometry that gets you into big tires. I run 54mm 2.2inch 27.5 tires on my gravel bike for example. It is fantastic. I run it at 17-24psi based on the terrain. Giant tcx advanced sx.

Modern gravel bike disc frames fit old non-boost 27.5 mtb wheels perfectly. 27.5 non boost is dead so you may get a deal on a nice used mtb set. I put some nice syncros wheels from my scott spark on mine with fast conti speed king rs tires. They even worked great tubeless.

Other frames like the new norco search will even fit 29x2.3. You can put on some fast xc wheels and crush it.

Finally, my 2016 scott spark 27.5 has near identical geometry to my giant gravel(cx) bike. It is literally a drop bar away from being a dual suspension gravel/xc bike (i can lock out the suspension when required).

Long story short... the hardtail xc bike of yesterday is a rigid fork and drop bar away from a gravel bike.

A modified hard tail 29er makes a perfect adventure / gravel bike conversion. I put a rigid carbon fork and drop bars on a old giant xtc.... super fun bike