We were away for awhile, but back now!
I grew up as on only child and used to work 2-3 horses per day - apart from my mum, I didn't have anyone to ride with and used to train for show-jumping and endurance riding so a lot of the time I'd be out riding for miles on my own. All the horses just learnt that they had to be OK out on their own. Each horse was always peppier when we headed for home, but I can't say I ever had a hard time riding out on any of ours. My pocket rocket endurance horse shied at anything and everything but he did that even if we were riding out with other horses, funniest was when he shied at his shadow. And yet he'd let me crack a stock whip standing up on his back. Go figure!
KDOGG331 - my advice as someone who grew up with them and gives lessons, enjoy the freedom of getting lessons on an experience horse. You don't have any of the responsibility or expenses to start with. Get confident, get fully set up for a horse and then find the right one. I grew up with horsey parents who had grown up with horses but weren't "Accomplished" riders by any means - we didn't have a lot of money so I ended up getting an unbroken 5 year old pony when I was 8 years old, she'd a reputation for being naughty with her green owners. We broke her in, mum rode her out the first time and the second time I rode her. Best pony I ever owned, taught me a lot BUT it was also the exception not the rule. She was in no way a push button pony but man could that pony jump. She was amazing. She got me off a lot and I used to get so frustrated. I never ever had a push button horse, we just could never afford them.
My farrier was saying a lot of the ponies he shoes are owned by non horsey parents. He says that my kids have such a huge advantage having myself, a horsey mum, plus horsey grandparents. I broke in a homebred Arabian colt when I was 15, he unfortunately didn't grow tall enough for me but he's been so well handled over the years (and gelded) that he is now a push button horse that my girls are learning to ride on once they've gotten the basics on their ponies.
We have the distinct advantage of years and years of knowledge, a good solid property completely set up for horses and the horsey blood running in our genes.
My SIL had the opposite, grew up with non horsey parents and ended up with some really crazy horses, one of which hurt her pretty badly. She's now got kids and has ponies and we were just discussing how her kids will reap the rewards of not having to suffer from rookie mistakes of non horsey parents.
Anyway, sorry for rambling but my advice would be to get really confident, offer up your time at your local barn to do some of the "behind the scenes" stuff, get as educated as you can and save your money. The better you can become at your riding and understanding of simple horsemanship, the better your experience will be when you get one of your own I can guarantee you. I'm not saying wait until you're riding Grand Prix, but the horse lifestyle is such a joy when you can do it right with the right horse!