Jeff,
I echo Jim's advice about the 2% of bankroll range. With a modest $500 bankroll, 2% is $10 which you can easily split $5 / $5 or $6 / $4 for starters. This is presuming you are betting into Win pools, which I'd say is the right place to start to get a feel for your win rate, number of losses in a row and a typical ROI%. If you don't need the money from the bankroll, you can let it grow (presumably) until you discover a bet size comfort level. The reason for 2% is that for any given bet it feels like such a small amount (e.g. $10 out of $500) that if you play perfectly and still lose 4 in a row it's no big deal, because you will later win 4 in a row. 20 bets at $10 / bet is $200 or 40% of your bankroll in play, so you still are making use of your bankroll reasonably fully. The 'unused' portion always provides an emotional cushion.
While collecting real money info (and info on your emotional experience), you can track what your hit rate would be on horizontal wagers like DD, Pick 3s, perhaps Pick 4s (i.e. comprising serial Win bets), then Exacta pools requiring the Place horse, which should most often also be within your top 5 Contenders.
I'd recommend tracking several hundred real Win Bets in cycles of 20 bets until your worst cycle is breakeven or a slight loss but no 2 consecutive cycles averaged produce less than a small positive. If your experience at this point is happier than these worst cases, consider opening another bankroll for Exacta wagers if your paper tracking shows you know how to identify the Place horse. For now, I'd suggest holding back on Trifecta or Superfecta pools because this requires including dodgier horses, some of which may not be part of your normal Top 5 Contenders, thus require a bit more latitude in contender selection.
Actually, if you are serious about long-term success, consider starting today at visualizing yourself as a 'professional', one for whom it is normal to expect a long-term predictable hit rate and double-digit positive ROI, and to bet decent sums in a given wager (e.g. $100 bet size). Keep your actual bet size small (e.g. $10) until it feels so normal to win (per your 20 race cycle records) that upping the amount to $12 is unnoticeable (then $15, then $20, etc) In a year, the amount will be $100 because it was small, comfortable increments all along, AND about 2% of a growing bankroll.
If you find you have made an ROI of, say, 60% on a given day or cycle (it happens

), consider looking at this as a surplus distribution which the short-term chaotic racing gods sometimes dispense. Mentally put this 'surplus' aside for those other days or cycles when the distribution according to your normal method is 0% or -20%. This absolutely happens and is normal. If over 200 races you determine that you make 20 cents on the dollar (just an example), those days when you make 50 cents provide you with 30 cents insurance against the next losing day of -10 cents on the dollar. Etc.
After a couple of hundred races and reviewing your strategy and emotional responses to winning and losing bets, I would recommend getting and studying a serious money management and bet sizing method described by Dave Schwartz in his
Horse Market Investing materials. Links to this can be found in the Library here:
http://paceandcap.com/forums/showthread.php?t=7104
Very best wishes!
Ted