I'm looking at completed auction prices on GB where Pre-64 Model 88s actually sold:
Pre 64 Winchester Model 88 Rifle .308 Win w/ K4 scope (about 90%) - 1 bid, $750
Winchester model 88 pre-64 .308 1960 (about 80%) - 1 bid, $659
9243 Winchester model 88 308 Win pre 64 (90%) - 1 bid, $700
There are also listings that did not sell (three of them are the same rifle):
Winchester model 88 Pre 64 nice 1959-1960 308 90% - starting bid $579
Winchester Model 88 .243 Pre 64 - 6 bids - $560, reserve not met.
Winchester Model 88 .243 Pre 64 - 6 bids - $810, reserve not met
Winchester Model 88 .243 Pre 64 - 9 bids - $859, reserve not met
Winchester Model 88 .243 Pre '64 (98%), Redfield 2-7 scope and spare magazine - $949 starting bid, no bids.
In terms of current auctions, with the exception of the above mentioned .284 with a starting bid of $2,349 (and no bids with only 20 hours left on the auction) the highest "buy it now" price is $1,350 for a mint condition .308, with another .243 at 90+% with a buy it now of $1,100. And no one's biting on those.
The least common calibers are the .284 Win and the .358 Win. The Model 88 was originally produced in .358 Win and was discontinued in 1964, so all but a single year of production of .358 Win Model 88s was pre-64. The .284 Win was introduced in the Model 88 in the middle of 1962 which means there was only a year and a half of production of pre- 64 .284's in .284 Win, which makes it a fairly limited production item.
However, based on current market values, asking even $1500 is probably asking too much unless it's in near mint condition and you can find an interested collector. That could happen with an 85-90% Model 88 in .284, but I doubt it. In that condition, your target market is a hunter who really wants a Model 88 and really wants one in .284 Win. At a minimum you'll probably need to list it repeatedly before you find someone that wants it that bad.
A better bet if you want to move it quickly is start with a low initial bid price around $400, set a $1,000 reserve and a 10 day auction and see if you can get enough interest to get a bidding war going.