This is a great question, it's hard to find the balance between finding your financial feet and keeping your battle stats progressing. There are several different options you can take, each with pros and cons.
Firstly, you can devote as much money as possible to happy jumps and worry about finances later. You'll need to set aside money for donator packs (if you're not buying them with real money/subscribing) and for PI rentals, and apart from that dedicate all your money to happy jumping until you're at about 200k for each stat.
Another option is the opposite of this; putting happy jumps off and using your money to make more money. This looks like continually increasing your bank investments, investing in stock benefits, and maybe starting to trade if that's something that interests you. Once you've secured some stock BBs and a decent amount of cash in the bank, then you can start happy jumping.
Most players would agree that neither of these two extremes are great options. To stay competitive you need to keep your stats going up quickly, but money makes the world go round and the more money you have, the more effective training becomes. A great alternative to happy jumps is choco jumps; they're much cheaper and you can easily throw in a couple a week to keep your stats growing steadily, gradually saving up for either stock BBs or bank investments.
Doing happy jumps also becomes much easier once you're in a 6 or 7+ star Adult Novelties and can get a few e-dvds a week. This means you don't have to dedicate money from flying into your happy jumps if you don't want to. If you can land a spot in a 10 star AN, they also become doubly as effective. Very handy if you have the working stats.
Ultimately, what you choose is going to depend on your preferences and priorities. Personally, I would advise getting at least a few stock BBs before committing all your money to training. Getting your stats to above 200k (happy jump range) is very important, but not at the cost of some diversified income, in my opinion.
Also, buying a PI is a relatively late game investment. Renting is fine and should probably be put off until you have a good number of stock BBs and I would say 2b in the bank, but some more experienced players might disagree on that.
Here's some links which might help:
Bug's Stock BB Guide - which contains a constantly updating API of the prices of stock benefit blocks and their time to break even, as well as a definition of them if you're not sure what they are
Choco Jump Guide - if you don't know what a choco jump is.
Best of luck!