Hi there and welcome! I am sure other more experienced people have great advice they are ready to give, I can give you some perspective as a fellow beginner.
First, the type of skate. For brand new adults wanting Jacksons, if the person is average size, I like the Jackson Elle or the Freestyle. They are more middle of the road as far as boot stiffness goes. Generally, the higher the level boot the more stiff and supportive it is. The bigger the jumps, the more support you need. The competitor is a pretty high level boot and may be difficult to break in. The exception to this can be if you are a heavier skater, you may need a stiffer boot to help support you weight.
Most people like to try on a couple of different boot brands to see if they prefer one over another. If you feel good in Jackson's, go for it, but try to get your foot measured by a professional so you end up with not only the right length but the right width. Regarding price, the Elle comes with a blade and will keep you in budget, if you go with higher level boot and put blades on them you will well exceed $300.
So, everyone wants to know how fast they will progress, how fast they "should " progress. The answer is, it depends. On many things, ice time being a major thing. I have been skating a year, but I could have skated an hour a month or ten hours a week in that year. You can see what a difference those two scenarios would be. The other factors are, your age and any health concerns, natural ability, previous experience, kind of lessons you take and how often you take them.
The good news is that there is no "should " as far as progress goes. It is good to set goals, but make them realistic and enjoy the process, enjoy your accomplishments. To give you an example of my own progress, I am 42, I skated at age 5 and 6 and not much after that until January of this year. I have issues with my back that limit my ice time. I slowly worked up to about two hours at a time and that is as much as I can do in a day. I currently skate 6 hours a week. I have a very supportive husband who skates with me, and have made many skate friends who are also helpful. My husband and I would like to do ice dancing eventually and we have done some of the basics already.
I have a private coach but have only had two lessons, and they were working on my basic elements, my rink uses the ISI system for most beginners who want to test levels. I have done several group lessons with other adults, they have focused on power, edgework, position, strength rather than certain levels of skating because there are all kinds of skaters in the group. I don't want to say I am self taught, but I am very motivated to practice by myself or with friends and let my coach make sure I stay on track. I am nearly ready to test for my Beta ISI, I am perfecting my back crossovers before I do that. ..I am hoping to test in January.
So, that is me. If I were younger with less physical problems I might have made more progress, or maybe not, I have not been very competitive historically. Good luck in your quest, doing searches of this forum on topics you have questions about can be really helpful too.