To the OP, if you are looking at securing a £200k mortgage in the SE and only 1-2 beds, I imagine you are looking in town areas. Still it would be best to check
www.rightmove.co.uk and review the prices shown on there - you may want to consider getting that £200k stretched a bit further to a 3-bed semi detached, or some sort, outside of town areas. This will reduce your need to upgrade a handful of years down the line, but you will be scrapping convenience for future-proofing. You say you want to be in the right position for securing a mortgage in about a year, but it is never to early to look and get a feel for how houseprices change over the year.
At the moment it is difficult to say what the banks will be like in a year's time. As first time buyers you will get access to some good deals, but the days of next-to-nothing deposits are over. To secure yourself the best (i.e. lowest) mortgage rates, the bigger deposit you will need - typically at the moment the best rates are for 75% LTV (Loan-to-Value) meaning you need to cough up 25% deposit. It will be difficult at first (parents!), but will certainly make your life easier in the long run as your monthly mortgage payments will be lower.
If the place you want to buy is exactly £200k, that means finding £50,000 to wack down in the beginning. However, some banks are still willing to lend for 10% deposits, provided you have a good credit rating, and most at 15%+. Being first time buyers I am not sure how much emphasis they will place on your earning history.
To get an idea, you could head to town and get an appointment with an independent "all-of-market" (access to all) mortgage broker (check with agents - I found ours in, of all places, Choices! But he was brilliant), who will crunch the numbers and show you the options on screen, and tell you the likelihood of Bank A, B, or C willing to lend to you in your circumstances and for what% deposits.
With regards to other expenditure (redecorating, furnishing the place) - this will depend on what you come with/condition of the place in the first instance. It is unlikely you'll want to live in an empty house for longer then 6 months (about the time when the house-honeymoon period wears off). However, note that there are always Buy Now Pay Later options (i.e. Sony if you spend over £1,500 you get Buy Now Pay 12 months Later, DFS for sofas allow you to spread the cost over several years if necessary, and places like LX Direct also offer BNPL deals for everything else).
A good site to use for explanations on credit cards, loans, mortgages etc is
www.moneysavingexpert.com, but don't apply for anything if it is to supplement your spending and you'd struggle to pay it back/pay the minimum repayments - if you can't afford it, just wait until you can.
