Bob,
A Match 54 would be a good choice. I'd suggest getting the newest model that your budget will accommodate. If a rifle is advertised with a 4-digit number, the first two are the production series; 14 = 1954-1980 (1976-1980 is sometimes called 16), 18 = 1980 - 1987, 19 = 1987-present. Rifles just described as Match 54 tend to be the older 14 series. a 1903 (or the older 1803, and 1403) is not a Match 54, it uses the lighter, cheaper, and less desirable Match 64 Action; it's still a well-made and accurate rifle, but the trigger is basic compared to the Match 54, the stock is basic and cannot be interchanged (wich the Match 54 can).
I'm afraid there aren't many ways to check the bore/throat without a borescope. You can ask the seller what the round count is (if they know), or make a conservative estimate based on the age. With 14 series rifles, the bluing on the bolt handle wears with use; so a silvery handle suggests a high round count (or a lot of dry firing). If you only want to shoot at 25 yards, high mileage won't be that noticeable, but for 50m and especially 100 yards it can show as bigger groups or fussiness about ammo.
What you should be worried about is a bulged barrel. This is caused by the impact of two bullets in the barrel, usually where an un-charged round has stuck halfway along; the rounds expand on impact, and stretch the steel beyond it's elasticity, creating a small bulge. Look along the outside of a clean and oiled barrel, a bulge will show as a ring across the barrel. If you push a patch (or better a VFG felt) through the barrel, it will jump when it meets the bulge. A bulge invalidates the proof of a barrel, so it cannot be legally sold or transferred. A bulged barrel is unlikely to shoot well in the long term.
General things to look for: the rifle should look like it's been well cared for. It doesn't need to be spotless, but if it looks abused, it could be an ex-club rifle, i.e. high mileage, minimal maintenance. Beyond that, check that the 3-digits on the bolt face match the last 3 digits of the serial number; this is important as bolts are individually matched to actions. Look at the bedding/stock bolts. If the heads are chewed or partially stripped, this is not a good sign; it suggets a ham-fisted owner or over tightening, which can compress the wood over time, so the barrel becomes loose.
Specks of rust are ok, if unsightly, but extensive rust on the barrel is bad; if the owner couldn't be bothered to keep this clean and oiled, it will be worse elsewhere.
Scratches and dents on the stock are only a cosmetic issue, but cracks around the grip or bedding bolts are seriously bad. Walk away from anything with a cracked stock, unless you have a spare and are prepared to negotiate a big discount.