There are many answers to this question and it depends on each player's play style, so you will likely get different answers.
Increasing your battle stats is a good way to improve your character, possibly the best. You will increase them faster if you have more happiness and you will have more happiness if you live in a Private Island. So good thing to do would be to either rent a PI (many of them in Rental Market) or share one with somebody through marriage (look in "Properties" subforum). Private Island give you many benefits that castle does not, one of them being the Airstrip that reduces your travel time and reduces the cost of travel so you can make even more money by running flowers/plushies/weapons/drugs. It also has some other benefits. You can refill your energy and nerve once a day for 25 points (1.6 million) and that is also good for increasing your stats and nerve bar.
Also, money is often spent on drugs -- you already take some Ecstasy, but Xanax gives you better stat gains by increasing your energy +250. It is usually sold for around 850k in Torn. Many players spend their money on drugs. Keep in mind that taking many drugs requires you too rehab often in Switzerland in order not to get kicked from education or company. There are other boosters for getting more stats, but they will be too expensive for you right now -- read more about them in Hank's training guide as recommended by hijoe.
Doing crimes also improves your character. It would be wise to spend money on crime enhancers for some crimes such as Arson, Grand theft auto, Kidnapping, Murder etc. because they really improve your crime success rate and will help you increase your nerve bar faster.
You improve your character by being better in combat. Therefore, it would be good to buy some quality weapons and armour. There is currently a discussion going on in General Discussion subforum about which weapons are best under 100 million - the consensus so far is ArmaLite rifle for 20 million, Diamond Bladed Knife (950k) for melee. Also, Combat Armour is the best armour to have if you already don't have it.
What I do NOT recommend: gambling in casino. You will always lose more than you get. Don't waste your toughly collected money in such manner. I know it from experience...
That's all I could remember on first glance. Good luck and spend it wisely :)
Wait, what? When have all these property photos been updated? I am 95% sure that all of them were different when they were introduced, but it has also been a very long time since I last lived in the cheaper ones or actively explored them, lol...
Can some old geezer back me up? The old stock photos were different and also more blurry/grainy.
EDIT: Alright, found at least two in some old Torn City trailer video... but all of them were different... would be interesting to also find all of those and where they originated from
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