LPN/LVN is a practical/vocational nurse. The scope and pay are both a bit lower compared to a registered nurse, and job opportunities may be highly restricted in some geographic areas. It's a good option to get your foot in the door - particularly if you want to work outside of acute care. (e.g. home health, hospice, or long-term care). The main advantages are that the LPN is a certification not a degree (though some community colleges may offer it as a degree program), which means fewer pre-reqs, shorter-time to completion (less than 12 months for many), and less cost. This can also be a good way to find employment while continuing to work on nursing coursework for either ADN or BSN. (Some programs may allow students to test for LPN along the way to either of the other degrees).
ADN are associates degree level prepared registered nurses. ADN prepared RNs may do everything that a BSN prepared RN can do (more or less, there may be some very minor exceptions based on state or facility regulations). The cost of ADN programs is typically low, and coursework may be completed in 2-3 years. ADN programs are more likely to offer some flexibility (e.g. weekend or part-time options) for working adults. The biggest challenges are because they are lower cost the competition for seats can be extreme in some locations, making ADN seats potentially harder to get into than BSN in some locations. In urban environments with multiple nursing schools, employers - particularly hospitals- may hire limited or no applicants with an ADN or may require any new hires with an ADN sign a contract to complete a BSN-bridge program in a certain time frame (ex: 5 years).
How your stats line up will depend on where specifically you are applying (different schools may evaluate different criteria) and what area of the country you are in. In a competitive environment it can be difficult to get into nursing programs
at all levels. In a less competitive environment you may have your pick of LPN, ADN and BSN programs.