I have put together a list of players that I think are particularly useful at the 1-star and 2-star level. They vary in price from as low as Ashley Barnes at 31p all the way up to Ziyech at £12.14.
The full list is here: Key Bronze picks
If you do have a smaller budget there are plenty of cheap options. Below I have put together 6 examples which together can be picked up for less than £5
*Prices correct at the time of writing (4/1/2021)
Goalkeeper - Robert Sanchez -Brighton 1* - Sell price 77p
A goalkeeper at 1* is a great enabler in star restricted contests. Goalkeepers tend to pick up consistent scores so it is hard to find one that is a regular starter in the lower star categories. Now Sanchez seems to of sealed the starting spot for Brighton, if you are struggling for a 1* for your Bronze teams Sanchez could prove a very good pick.
Defender - Walker-Peters - Southampton 2* - Sell Price 57p
A player I quite regularly use in contests all the way up to gold. Capable of plenty of successful dribbles and plays in a side that picks up clean sheets. Arguably as good a pick as many defenders at a lot higher price.
Defender - Alioski - Leeds 2* - Sell Price 68p
A defender who likes to get forward and has an eye for a goal. With a Leeds side who often scores for fun, Alioski is my pick of their defenders. Has 21 goals in 140 appearances for Leeds
Midfielder - Ruben Neves - Wolves 2* - Sell Price £1.01
A player who has a decent base score but not always a standout pick. However, with Jimenez out the side, Neves should be on penalty duty when on the pitch. With Wolves having tricky forward players that pick up their fair share of penalties this gives Neves plenty of value
Midfielder - El Ghazi - Aston Villa 2* - Sell Price £1.26
One of the in-form premiership players. Not always a regular start for Villa in the past but currently playing too well to drop he's also a player that's hard to look over for the contests. El Ghazi tends to pick up plenty of successful dribbles and is also currently on penalty duty. With Villa in this form, he's hard to look over.
Forward - Caveleiro - Fulham 1* - Sell Price 61p
Cavaleiro seems to of sealed the role as penalty taker for Fulham and also takes corners which makes him a very handy 1*. He's not someone who can always be relied on to pick up big points in a struggling Fulham side but their performances have improved of late and with the potential for a penalty can make him a great differential.
Good luck in building that collection.