Welcome to the site and the sport of bowling HillHawks02. I see you are in Maryland, where at in Maryland. There are several of us on this site in the area and might be able to point you toward a league that might suit you. With summer starting there are plenty of fun leagues that are a great way to get experience in leagues.
As for your questions.
Weekdays/Weekends? I do both. When I started bowling it was on a Saturday mixed gender league with my brother and his wife. I like bowling with them and this is really the only time they have to bowl since they have 4 boys who play some sport or another throughout the year and most games are weekday evenings. My weekday leagues tend to be more competitive mens leagues.
Team Uniforms? There aren't many leagues around that do this, some teams in one of my leagues do have team
shirts. I like it and my Tuesday team has been talking about it. I think usually only the real competitive classic leagues require this.
What type of prize? Most adult leagues are money leagues. There are some merchandise leagues where you can get a ball, bag or other bowling accessories and sometimes other stuff like jackets. Everyone gets these in those type of leagues so how good you do is irrelevant. Thats depending on what the league is set up for. There are also vacation leagues and others like Brandon mentioned.
How much do you pay? My leagues this past season were $18 a week for my Saturday mixed, with $10 or so a night going to pay the center for lane usage, around $.40 to pay the league secretary for his/her job and the last $7 or so going into the prize fund that gets broken down differently based on team standings. My Tuesday Mens league is $20 a week with a similar breakdown just more money going to the prize fund. Some leagues are more and some are less depending on the league and how much the members of the league are willing to pay. I'm going to different leagues next season on the same nights but expect to be paying a little more a week.
Members on a team? I've never bowled league that wasn't at least trios (3 members per a team) and those are usually any summer leagues I do. My fall/winter leagues have been 4 person for the most part, next season both leagues will be 5 person. Anything less than 3 is too fast paced for me, and even then the trios leagues are a bit on the fast side. I prefer the 4 or 5 person leagues. I have done some doubles tournaments and that is a quick pace.
As a new bowler a fun handicap noncompetitive handicap league would be best to get started and learn how leagues work and some of the etiquette of bowling in a league environment. There are very few scratch leagues in the area so you should find plenty of handicap leagues. The aforementioned merchandise leagues might be good for over the summer and then through them you might meet some bowlers that know of a fall/winter league that would suit you.